I can only speak for myself, but here’s what I mean when I say ‘soft mechanic’.
Partly, sure, mechanics that aren’t “hard”/numerical: Conflict phrases in Polaris, Contempt tokens in TQY, etc.
But mainly I mean… meta-mechanics, I guess? Instructions and directives which operate at the player level, and engineer the shape of the conversation the game produces.
That might be directions on how to conceptualise the game. (AW 2E: “Whenever your [as the GM] attention lands on someone or something that you own—an NPC or a feature of the landscape, material or social—consider first killing it, overthrowing it, burning it down, blowing it up, or burying it in the poisoned ground.”
It might be directions on how to structure the game’s conversation. (Blades in the Dark: “Which actions are reasonable as a solution to a problem? Can this person be swayed? Must we get out the tools and tinker with this old rusty lock, or could it also be quietly finessed? The players have final say.”)
It could be instructions on what to say. (In Stonetop, during the Introductions step of character creation the GM is told to ask a lot of questions. And specifically, in addition to questions they’re naturally interested in, they’re actively directed to ask about the character’s families, their livelihoods, their housing situation, whether they’re literate. This is a very powerful way to communicate tone and nudge the initial picture of the world the players form).
Or it could be direction on what kind of things to say. (In my game The Blood Must Flow, here’s character creation: For each reveler, choose a craft - butcher, winemaker, orchard-keeper, etc - and think about their look, incorporating colour, texture, smell, animal imagery, etc. Starting with whoever last touched the soil, introduce your reveler. Describe the gift they bring to the feast: what it is, how it looks, how it was made.)
I’m sure there’s countless other examples I and others could think of. But yeah, for myself, that’s what I meant: player-level instructions that direct behaviour around the table and in the conversation of play.