RDP GPU acceleration should be available (on Windows, at least) with the right quality settings. AFAIK nothing API-wise prevents GPU software from running. That said, RDP is an edge case few software developers bother testing so I'm sure there are lots of programs out there that ignore edge cases when it comes to rendering APIs.
It's not optimised for games, though. Something like Parsec would be much better for interactive stuff like that, or maybe something like Moonlight for Nvidia cards if you're looking to go without closed source software.
RDP also supports streaming regions, including the entire desktop, as hardware-encoded video. It was introduced 9 years ago[1].
As for performance, I've been playing full-screen games over it. Latency sucked when I was literally on the opposite side of the earth but if the bandwidth was there it worked fine.
From work to home RDP is typically indistinguishable from being local for me.
It's not optimised for games, though. Something like Parsec would be much better for interactive stuff like that, or maybe something like Moonlight for Nvidia cards if you're looking to go without closed source software.