In Norwegian, most genre names are very straight-forward, like bilspill (car games), slåssespill (fighting games), rollespill (role-playing game, literally "role games", but the word "rolle" in Norwegian implies the role-playing part), horrorspill (horror games), partyspill (party games, platformere/platformspill (platformers/platforming games). Shooters are literally skytespill (shooting games), with a distinction between tredjeperson (third-person) and førsteperson (first-person).
Some genres are described in singular terms, like RTS and RTT are often called strategispill (strategy games). I don't play RTTs enough, so there might be another term but I've never encountered another term for it. I'm not sure if there's a term for beat em ups, but I've used arkadespill (arcade games) for it, and I've heard others use the term as well.
Stealth games could be called snikespill, but I never hear anyone use that term anymore. People just say "stealth" instead. Everything action-based that's not a beat em up, fighter or shooter is called action game or action-adventure (action/action-eventyr). Stuff like MOBAs, MMOs are referred to as such, although calling MOBAs "DOTA clones" is pretty common.
