Also not sure if it'd just a licensing issue. I think all the games might very well be modded to run on Stadia servers. May be the renders are optimized to send out compressed video over the wire instead of a video output. Totally speculating but I think it's likely that the games need to be integrated into the Stadia platform somehow.
iirc they support games made with certain engines out-of-the-box. Ironically, I think I heard that it's the Unreal Engine (sorry, Epic Games Store...). AC:O and BL3 seem to support that theory.