I don't think anyone with a phone running 2.x can run games. I have an HTC One or whatever (4 years old; got it from a friend) and I could never ever imagine playing a game on it. Even the home screen lags!
The problem lies with the hardware, I think. Truly, there's never a smooth moment with my phone. Sometimes it hangs for a minute. Random shutdowns and similar bugs in software as well.
I've got an old cheap 4 year old Acer phone running 2.3 as a backup phone and it plays lots of games fine. Sure not games using a lot of 3d graphics or games which require very precise timing, but it plays lots of other games.
Everything that matters, besides the existing graphics, sensors and audio APIs, can be built with standard C++ libraries.