It's the operating system or vukan/mantle ?
Don't remember if linux has or have some kinda of direct X.
"Beating" the amd dreams to deaf
Proton includes dxvk -- DirectX 9/10/11 to Vulkan translation; and vkd3d (DX12 to Vulkan translation). These can be installed in Wine. For that matter, apparently they can also be used in Windows; Intel for instance is shipping Windows drivers for their newer Intel GPUs that are DX12/Vulkan only and letting DX9/10/11 games run with dxvk.
There's ALSO an older layer, in Proton you must set "PROTON_WINED3D=1" in a startup script (and it's default in wine if you don't install dxvk or vkd3d), it'll have a go at running DX9/10/11 games through OpenGL. There's probably no reason to use it unless you're running an older card that does not have working Vulkan support. I used it on my friend's old Sandy Bridge system and it worked fine though! (Amusingly, in Windows support for Sandy Bridge stopped 1 month before DX11 shipped, so in Windows it supports DX10 while in wine it supports DX11. Good thing, too, since Unity upped their minimum to DX11 there's many many games that require DX11 now even if it's a not-at-all-grahpically-demanding side scroller.)
I'd like to see a comparison to the reduced footprint (both in CPU usage and storage) Windows that can be created with available utilities. You handheld gaming system probably doesn't need to know about domain networks, for example. Those chunks and services can go. You'd want something that used on the current Xbox but not as bare bones.
To be fair, though, there are also lite Linux distros -- as fast as Arch, etc. are they are not even considered lightweight distros compared to some. That said, the "full fat" distros just usually use slightly more RAM, don't run excess processes that burn through CPU time & disk I/O (very often... they will occasionally spend a few seconds checking for updates and such, if that's not turned off.) Would be interesting to see though!
I can say (running both in VirtualBox) compared to Win10, Win11 is MUCH faster to boot, and although Win11 still churns through CPU and disk I/O for quite a while on bootup doing virus & malware scans, windows update, the totally seperate from Windows Update updaters for Edge, I think one for OneNote (edit: Probably OneDrive now that I think about it..), and maybe another one or two others, and the Windows Store app updater.... it's still a lot of excess activity but noticeably less than Win10!