Hi Adam,
Stonetop is still in production, but I’ve got my nose to the proverbial grindstone. You can find most of the relevant rules in the documents at the bottom of that blog post. Specifically, check out the Moves & Gear and the Stonetop Steading Playbook. We’re in closed playtest right now, but it’ll likely switch to open in the next month or so. Let me know if you’ve got a group that’s interested in playing!
The game is definitely rooted in D&D style play: you go on adventures, often exploring ruins and killing monsters and saving kidnapped villagers. The moves for violence outnumber the moves for social interaction.
But, as @calris says, the game’s premise (and the class playbooks) are rooted in a specific home town. They’re going on expeditions to kill monsters that threaten their home and neighbors, or acquire resources they can use to prop up the town, or to rescue someone’s lost nephew… that sort of thing. The PCs themselves often have big personalities and big goals, too, but the bulk of the game gets pushed and pulled by the needs of the community.
Rules-wise, the main social mechanic is Parley:

You’ll notice that it doesn’t give the PCs any ability to control minds or force agreement. It ends up being an information-gathering move a lot of the time, revealing how you could convince them to go along, and then it’s back on the player’s to decide whether they’ll do that.
The town itself has stats: Fortunes (morale and general well-being), Population (growing or shrinking), Prosperity (material wealth and trade, quality of gear PCs can get), and Defenses (militia’s skill and readiness). There’s a subtle economy between all those stats, but it all serves to generate threats and opportunities and give the players projects to work towards.
There aren’t mechanics for tracking popularity or factions per se, but fictional positioning goes a long way here: as the Marshal, I can probably get everyone to go along with building a palisade, as long it’s not taking bodies away from spring planting or fall harvest. But if the Seeker wants to get a workcrew to help him build his crazy magic weather-vane, he’ll need to do some convincing.
The game also borrows from Apocalypse World 2e and has you create problematic NPCs and factions and afflictions as “threats” with stakes questions and/or countdowns. Because these people are your neighbors, you can’t just ignore them*. You can’t just kill them or beat them up, so you have to work with them or around them, and factions and popularity and politics can come into play there, too.
There’s a generalized Make a Plan move for designing long-term challenges, based largely on the Savvyhead’s workshop framework, so if you wanted to undertake a long-term project to, say, establish a town council and get yourself elected mayor, you could.
Mostly, though, the social interactions go back to that one Parley move: it really does a lot of heavy lifting in the game.
Happy to answer any questions you’ve got, about this or the linked materials!
*(Or, I guess you can. But that’s how you end up with a nascent cult kidnapping refugees and sacrificing them for power out in the Great Wood.)