Answer from Fist of Awesome developer

Fist of Awesome

"Hi Jim,

I'm not sure if it works on the Shield unfortunately. I don't have one (yet anyway) so I'm afraid I have no idea. FIST OF AWESOME does support gamepads on regular Android though so there's a pretty good chance it'll work, but I have no way of confirming that.

Thanks for getting in touch, hope that helps in some way!

Nicoll Hunt

Head Honcho - I Fight Bears"

UPDATE

I am going to download the game on Sunday & test it.  Then I will let you all know.

-- Jim