Linux

Without Nvidia's proprietary driver (nvidia-dkms), you're probably using the independent, open source Nouveau driver for Nvidia cards. Nouveau has issues (performance at least, but also stability on some hardware), even on X11. I don't think it supports Wayland, and there are no mentions of Wayland anywhere on the website.

As for why you need nvidia-dkms: the proprietary Nvidia driver isn't open source, and needs to be compiled and linked on your machine for legal reasons.

Nvidia now publishes an open source driver that works on some GPUs (open-gpu-kernel-modules) that could end up in the mainstream Linux kernel, eventually. Nvidia hid all of its special sauce in firmware starting around the 20xx series of cards (and also for the 16xx series), so it seems they have decided to finally open up their drivers. For older hardware (up to 10xx) the special sauce is packaged in software, so Nvidia has kept the code for those devices closed source.

As for the "fullscreen videogame": in a way, that's true, both for X11 and for Wayland. The difference is that X11 has existed for longer, and Nvidia has provided the necessary hardware acceleration features for X11 for longer as a result, ironing out a lot of issues. X11 also allows them to add their stupid arbitrary limits (Nvidia put a hard cap on the amount of displays you can drive using their driver on consumer platforms for no well-explained reason). For Wayland, for years Nvidia refused to implement the normal spec, and instead decided to only implement an optional side feature that only Gnome really used, just to get Nvidia hardware working. They changed course a while ago, but Wayland + Nvidia is still a mess even with the latest drivers and code.

Nouveau has been developed for X11 from the start and the project is moving very slowly. That's not because the project doesn't care, but because reverse engineering GPU hardware is extremely complicated. It took a while to get the 30xx series cards to the point of "boot and show a terminal", so don't hold your breath for Wayland support.

Why do you need hardware acceleration for GUI? Well, technically you don't, but you probably don't want one or two cores being eaten up entirely by rendering your screen. Performance will be terrible, the GUI will stutter like crazy, and if you're on a laptop, your battery will drain fast.

TL;DR: Nvidia + Linux is always iffy, be glad X11 works well for you if you don't use the proprietary driver, because that's far from a given.