Yes, they can play native games. The new Teenage Mutant Ninja Turtles game has a Linux/arm build that works on previous generations of this device, Beats of Rag

Yes, they can play native games. The new Teenage Mutant Ninja Turtles game has a Linux/arm build that works on previous generations of this device, Beats of Rage works, there are native builds of Super Mario 64, Another Metroid 2 Remake (AM2R), Half Life, etc. They are targeted at emulation, but it's just a small ARM computer running Linux, so you can really do anything you want (within the limits of what the hardware can run, of course.)