I have just watched a video interview with the programmer for the SNES port of DOOM:
I did not note the timestamp, but at one point he mentions how he wanted to have "as many feature icons as possible" on the box art, and said how the game supported the Super Scope, the mouse, XBAND, etc.
Afterwards, I tried to look up both videos of the mouse in action and tried to view scans of the box's front and back, but saw no mention of mouse or Super Scope support.
Shouldn't there be some video showing this off if it actually supported those controllers? It would be amazing to see how "smooth" the player moves with the mouse.
I also did not see the game listed in a list of mouse-supporting SNES games. But then why did he say that in the interview? It didn't seem like a joke to me.