Interesting. I will say I suspect still this is to make the controller act as a mouse or keyboard somehow, which steam can do.
One interesting thing is that it says in the bug report, that steam also requires uinput, which is used to create virtual input devices from userspace. And maybe (speculating) you need that for XTEST to work on wayland or something, or maybe steam can use uinput instead of XTEST if it's not available.
Or maybe it's security-related somehow (Regular programs being able to create virtual keyboards is kind of a security issue).
For me the output of getfacl /dev/uinput will list my username with read/write permissions. I have no idea what is responsible for giving me this permission but there it is.
Can you check with getfacl in both sessions?