Update:
I've updated the drivers using the ones from the Intel page. This had no effect. I'll attach the new output from Dxdiag.
I'll try and see if I can get any previous iteration of the game to run, using the functionality of the itch. io launcher. I'll be using the "no-media" version for convenience.
Edit: Okay, #42 (published on September 3, 2019) works. That's the very earliest iteration I can find on itch. io, using the launcher. One thing that struck me as odd was that the top bar of the game window was way up and to the left, to the point it was off the screen entirely.
I'll be updating this post with more findings.
Edit 2: The latest version of Quasar that runs is #60, published on Oct 11, 2019. The game starts fine, and I can even load the example game, but there's several problems even so.
Clicking on Settings will crash the game.
Clicking on System Map will freeze the game.
Advancing time (via the controls on the Economics screen) will freeze the game for a moment before updating. Just how long it spends frozen seems dependent on by how much is being advanced, although this particular issue may have more to do with me using an earlier version.