By "Alpine Linux", I meant "the stuff that Alpine Linux usually ships with", which I doubt is rich enough to support everything that Steam needs, plus you're not going to get a nice package to install as you might on another distribution: https://developer.valvesoftware.com/wiki/Steam_under_Linux. So I'm pretty sure the answer to the original question is still "no, not yet", though I don't think it is "no, not ever".
You still don't seem to get it: this project happens to ship with an Alpine Linux userland, but you can just build it with Ubuntu Core instead, it will just be insanely large. Alternatively, you can just download Ubuntu Core and either replace the Alpine parts or put it in a chroot. Steam isn't going to run because it doesn't have a graphics layer, but it isn't because this is somehow--and I mean right now as it is installed on your phone without even having to reinstall it--in any way tied to Alpine Linux.
I do realize that this is using Alpine because it's small and easy to package, and that it's not in any way tied to Alpine. I wouldn't be surprised if you could do this on device right now by nuking the folder (which is helpfully exposed through Files) and unpacking a Debian filesystem into there. And I doubt any games will run at all, even if you do this, because emacs doesn't work currently due to missing system calls. My response was basically saying that along with "Alpine Linux likely doesn't support Steam, so if you download the app you won't be able to install it easily."
