For me, I got mine to work by assigning all buttons to actual xbox button names rather than specific actions

Worked out of the box for me...

EDIT: ... although it might be necessary to enable "SteamInput" in the game settings on the Steam client. I have some vague memory about needing that for this game, but I'm not entirely sure.

There definitely wasn't anything fancy to do, like manually assigning buttons -- stuff like that sounds as if someone is going through the keyboard/mouse emulation, so the game isn't even using the controller...

Mine was not working at first but when I enabled SteamInput it worked.

yeah i fixed it. just gotta play in big picture mode with Controller input enabled

Easy, I was facing the same issue.. But it happened with the other SAO as well so I made the same thing.. Went to picture mode settings activated generic controller and Playstation controller (need to mention that my other controller that is not Xbox needed the exbox controller settings for some reason activated to work) then start the game and voilà! Experiment a little bit since it seems that the version or the brand of controller works differently with every setting activated.

Have fun!

There’s official controller layout for the game. Go into big picture, select sao hr, and click the controller icon, then select layout. Theres two types, one for Xbox one and for Xbox 360.
If you enable generic controller option, when you play other games it will also effects the gameplay of other games.

Steam Big Picture and config