I believe PICO-8 doesn't require a gamepad, but is designed with them in mind. I tested on a standard keyboard, so I'm unfortunately unsure of what's causing your bug!
I tried again in an icognito window and it worked so it must've been something on my end! Cute little game, I always love to see people learning new things and experimenting with stuff in game jams so it was cool to see you take the opportunity to learn PICO-8