I really like the idea. Using long-forgotten card game for conflict resolution sounds great. And I’ve got to say that the overall impression after the first read is positive. There are things that could be improved though and I’ll focus on those. I’ll give your question about the stats some though when I go through the document for the second time, so what follows are just some general thoughts after my first read-through.
I have the same general problem I had with @Radmad’s game - you’re using language specific to card games without explaining it. I have a fairly decent grasp of English and neither tricks (Hesitation at the Gate) nor poker checks (Leadtown) were obvious upon reading. So even though I played bridge, none of the players were speaking English and “tricks” simply never entered my vocabulary. Same goes for poker checks. You mean chips, right? 
I think that the obvious-o-meter should be based on a quick search for a term in Google in the incognito mode. This isn’t needed for the vocabulary you use in the prose, as this can be inferred from the context, but for terms that have mechanical relevance I feel like this is a must.
Leadtown cuts on explaining what an RPG is (probably a good idea) but goes further than that and doesn’t explain what scene is yet using it as early as in “The Banker” section. I’m not sure this is fair given that scene in various games has a slightly different duration and significance and knowing what designer intended may be instrumental in replicating the desired play feel. You’re also later talking about “scene resolution” in the context of ECs but as a reader I have no clear understanding of what scene is at that point. It’s explained in “The Grand Finale” that scene lasts for 5 minutes but it’s not clear if you’re talking about in-game time, wall clock time, or both.
This extends to talents available “once per game” (something you stress twice in a single paragraph) - what does “a game” mean in the context of Leadtown? In “The Grand Finale” you talk about session - is that a synonym for a game? There’s also a matter of using the term “tags” in the “Where ya in from?” section even though there is no mention of what tags are by that point.
I find your language around role and character types a little muddy. DeReel already mentioned “AKAs proliferation” which summarizes the problem well: you’ve got a number of terms that denote the same thing. But there’s also an information flow problem: I don’t think the distinction between players (humans) and characters is clear enough.
You should probably more vividly explain the two types of participants first and then all the types of characters in play. This should include Enemy Characters which, for whatever reason, are mentioned long after it seems like you’re done with the game specific lingo. I think it’s also important to, at the very least, foreshadow early on that “at different times Banker Characters will be played by Punters when
the Punter’s character is not in the scene” - if not spell it out right the moment you introduce the character types.
Only Banker-controlled characters have abbreviations (BC/EC) and PCs are not mentioned when characters are described. And then, out of nowhere, GCs are dropped elsewhere (and NGC too - what?) and I have no idea what they are (all characters or Punter-controlled ones only? are player controlled BCs GCs?)
Also you should probably pick what’s the primary name for whatever and stick to representing this name Capitalized or bold and figure out what exactly these terms represent. In “The Punters” section you’re introducing the concept of Census Sheet dropping “archetype” in the brackets and later explaining that it’s a character sheet. But then you’re closing this section by using the word archetype again. So now I don’t know if this is a block of stats or a template of a character to play. Or both. It may seem petty and nit-picky but this really affects the clarity of your writing.
I do a lot of technical writing and the mechanism I use to get the consistency I want boils down to writing stylistic rules down first and then religiously following them. So for example I’d decide on domain specific terms to always be capitalized plus the first time they are introduced they’d also be in bold. So if you’re introducing some term and use previously unmentioned terms to describe it, you know have to reorganize your document (the rule should be: single bold term per paragraph, that way you know you’re not creating lingo soup).
This will sting at first and you’ll be tempted to break your own rules here and there, but don’t. Reword and reorder your text to never break the rules. It will be much easier to follow for anyone who isn’t intimate with your game (which is the target of your writing after all).
The “Sand and Sharp” and “Scene resolution table” sections are impenetrable upon first reading. I had to go through them several times to grasp the basics of conflict resolution. Gunfights seem complicated but I think I could follow the description and understand the basics (the example provided helps too). They seem visceral and lethal as they should. The only thing that perhaps could be better is if gunfights were resolved real-time, i.e. as players draw the cards. But it would be hard to do given the skill disparity between characters so this seems like the next best thing and I like it a lot. 
And lastly: I’m not sure this game enforces the stated premise. I mean, whether it’s about “accruing power, wealth, and justice” (BTW: can you accumulate justice?) or “reaching your goal by working through the establishment…” I don’t see how rules support this. Rules don’t contradict this, sure, but there seems to be very little emphasis on the theme beyond some archetypes having goals alluding to it. There is no social currency in the game that would affect character’s road towards their goals. In other words: game doesn’t feel as tight as it could be.
I guess chips could be a stand-in for fame/infamy but this strikes me as a missed opportunity for embedding social themes into core game mechanics. Bonds probably immediately come to mind as a social mechanic to use but I don’t think they fit the theme that well. There’s probably something else that could be employed here. I mean, even EC rules hint at relationships being fragile, so perhaps some sort of IOU mechanic/currency would spice things up? I don’t really know what the solution here is but I’ll try and focus on this when I read through this again, trying to respond to your stated question about the stats.
Some other random thoughts and nits:
- How is adversary (page 9) different from EC?
- There is no inherently Black archetype, which is a shame.
- Tags are never explained.
- The word “trait” is mentioned exactly once in the document. I think it should be something else.
- Scene setting table goes from 1 to 11 - shouldn’t it go up to 12? Also: what about jokers?
- You’re talking about “How do I Create a Punter Character?” section in “The Punters” but the section is actually called “How to build a Punter character”.
- When describing hometown, you code “wanderers” as jokers; later on in the character creation steps you switch jokers from wanderers to immigrants - I’d cut the mention of suits+joker in the hometown explanation and keep a single source of truth in the document
- A compressed timeline of important events and visitors in Leadtown would be nice. Real or fictional, doesn’t matter that much as this would mostly serve as a reference for what sort fo changes were happening in the town.
- I’ve said it before when going through “Hesitation…” but I’ll say it again - you should keep your text, the master copy of it, unformatted. If you publish this on Google Docs enabling comments from people who have link to it (make a copy of it first, just in case!), you’ll be able to gather feedback much easier. There’s a bunch of typos and style problems that are easily marked inline but are sort of a hassle to point out here (even though e.g. DeReel did - kudos!) When asking for feedback, make it as simple as possible for others to provide. Even if this means you’ll have to build a throw-away, formatted version for your playtesters, chances are it’s worth it.
- Some scene setting suggestions: railway station/railway construction site (pre-1880), hospital, mill, burro racing/gun show location (not sure if carnies existed already), cave/abandoned mine, abandoned shack in the woods.
- Mention early on that Faro is used not only for conflict resolution but also for character creation. I’d sell it as “this way you’ll familiarize yourself with mechanics before they become critical in-game”. Right now I sort of feel like “why isn’t this just a simple card draw or a dice roll?” - which isn’t ideal frame of mind.
- I’d consider ordering character creation so that pure Faro rules are used first (w/o any additional limitations or corrections for what you’re generating) so that players don’t get confused with that’s the real Faro game flow like. Ideally I’d mold the rules so that there are no exceptions and there is a single “type” of Faro played at all times, but I don’t know if this is doable. I’m not sure if reordering is a good idea though (it could break other things), it’s just something I’d test on new players.
- The “Player Character Death” section contradicts earlier statements WRT luck-for-chips price (3L => $5) indicating that death can be prevented by spending 5L. I’m also dubious about the cause of death table as this seems like something that should be directly tied to the scene type, no?
- “The Epilogue” talks about the secondary goals but these aren’t mentioned anywhere previously (just that characters have goals). This should be expanded upon in the character creation section.
