I feel like a moron for never seeing this after 2.5 years :-D. Thanks for pointing it out! Maybe I'll make a cute animation of the contraction for a loading screen. I'll make sure to credit you.
"Gamen" is one of those anglicisms that has made it into the language, with ugly but in this case useful conjugations:
Ik game met je (I (play a) game with you)
Hij gamet met je (he plays a game with you, this is especially nice because of the repeating "met")
Zij gamet met je (she *)
Wij gamen met je (we *)
Zij/Hun gamen met je (they *)