Just a bit of a technical update; this game really relies heavily on Steam Remote Play Together for its multiplayer (and who wants to play with themselves, really?) - amazingly, and shockingly, Valve have broken this.
The symptom will be that you join someone hosting the game, but all joining players don't appear to have any joypads! (keyboard and mouse still works tho…)
The good news it that they HAVE fixed it, but haven't made it public yet; if you need to get it working again, head to:
Steam -> Settings -> Interface -> Client Beta Participation and select 'Steam Beta Update'
Let me know if that fixes it for you!