I literally just did this, so I'm no expert, but I thought it was pretty cool. Thought I'd share how to do it as well as welcome any comments or ideas as I'm now thinking what I could do with this.
This isn't going to be a full tutorial - you need to have a Discord Bot and have your game/project already hosted somewhere.
Add Activity:
In your Discord App/Bot developer portal, scroll down to "Activities" and choose URL Mappings First. You just need to put the URL of your game in there.
Then choose Settings and you just need to toggle on "Enable Activities"
Open in Discord:
It has to be opened from a Voice Channel
Click Launch Activity. Your Activity will probably be at the top:
And then your game should open!
I believe there is a Discord SDK so that you can identify players in your game - like by their Discord Username and such - which I will probably see if I can get that working next.
I'm not sure if that would actually help to make your game multiplayer at all - probably just to act as your auth/identity. But I thought it was cool just to see your game in Discord this way and curious what this could allow.