"What is your level?"
Translation:Hvad er dit niveau?
Rank (in the military sense) would be "grad" (which also happens to be the word for 'degree' as in e.g. temperature). In this case it is more about someone's skill-level, e.g. at a game like golf or as an academic skill like math, languages, etc. The word 'niveau' can also be used for things like the level of water in a container etc. Your example of the video-game is pretty good I think, the word niveau could be used there, although (and probably for historic reasons) one often see "baner" (as in 'lanes' on a highway) used in that sense.