These games are a relatively tough sampling for Wine to handle. I wanted to give it a good workout. Skyrim and ME2 are easy, Deus Ex is theoretically easy, DX:HR and Mirror's Edge are easy to run but tough to run well, I've never gotten JC2 or Worlds Adrift running in Wine (the former because last time I tried it Wine didn't really do DX10 yet), and TABG is no longer likely due to anti-cheat. This sampling is pretty DX9-heavy because I haven't yet gotten around to buying too many more recent games (I've got plenty of Steam backlog without buying more) and most of them I do own either have native Linux versions or are 30+ GB downloads.
On average, it's about as expected. There's room for improvement and troublesome games continue to be troublesome, but it does bring a lot of games into an entirely different class of ease-of-use.
This is with an R7 1700, RX 480, AMDGPU non-PRO, and 1440p.
It stores the Wine prefixes in Steam/steamapps/compatdata/[appid]/pfx/, one prefix per game. Even if you're not tweaking anything to do with Wine, that's useful to know for ini editing and the like.
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Deus Ex (the original): In the main menu the mouse bindings are wonky (left movement moves up and left, right moves up and right, down moves down and right). Weird, but once in-game everything's flawless. Every time until now I've tried to play it (including on Windows) something or other has been problematic, so this is a good showing.
DX:HR: It's good with Gallium Nine, but without it it's still stuttery enough to be barely playable, even on minimum settings. That's a failing grade in Steam Play.
Skyrim (non-SE, no mods): ~60 fps (max settings aside from shadows and reflections) is a bit weak, but latency and smoothness are top-notch. I don't remember Skyrim ever being close to this stutter-free even on Windows (though admittedly the last time I tried that was on a system with a lot less CPU power).
Just Cause 2: It looks like there's a bug in Steam Play's setup of the Wine prefix. It's probably easy enough to fix by Wine standards (though I haven't tried), but by the kind of ease-of-use standards we're looking at here it's a failure.
Mass Effect 2: Flawless.
Mirror's Edge: Stuttery, but I haven't yet found a way to play it that isn't, including on Windows. It's good enough for casual play and about as good as on Windows+Nvidia, but significantly worse than Windows+AMD and even that is pretty shoddy for speedrunning.
Totally Accurate Battlegrounds: They added anti-cheat (EQU8) since I last tried this, and that doesn't seem to get along with Wine.
Worlds Adrift: EAC works, so maybe my previous thoughts on Wine and anti-cheat are off-base, but it looks like it messes with DXVK, hanging the system's graphics badly enough that ctrl-alt-F2 doesn't help. I'm not inclined to blame DXVK; it isn't exactly the first time Worlds Adrift has done things like this.