How do cloud gaming services work?

Question

Windows

A few years ago, when Windows 10 was at version 1607 (then everyone switched from 8.1 to 10), I decided to run programs that require access to the video accelerator inside the RDP session. However, the programs could not work properly with the video card.
Now that the server is Windows 11 and the client is Windows 10 1909, I started remote access again. Video editing programs work fine, PhotoShop runs smoothly, blender renders 3D animations, and even games work. But there is a problem with the latter - in AnyDesk the mouse behaves chaotically, while in Microsoft RDP the mouse works, but it only allows you to rotate the character by 180 °.
How do cloud gaming services like PlayKey and Vortex work? How to run heavy programs and games remotely?