Trying another video game, this time
BoXiKoN, to try to summon the graphical issues. BoXiKoN switches the resolution of the display on the fly (I think probably to 640x480 but I don't know), producing vast amounts of glitches from the start, regardless of internal iMac temperature.
HollyTris summoned no graphical glitches on its own because it runs in windowed mode, not changing resolutions. Similarly,
Celeste didn't do anything, either, and runs in windowed mode.
I don't know how useful this new find is, but I found it interesting that BoXiKoN switching display resolutions did that. Switching display resolutions myself within MUI Preferences did not produce the same result.
Mac Mini G4 1.5 Ghz, ATI Radeon 9200 64MB, 1GB RAM