"The children are playing a game."
Translation:Børnene leger en leg.
I think a "leg" is something you physically do, normally (such as "Olympiske lege") such as sport or tag. One would "lege en leg". Spiller is used for things like board games and video games, one would "spille et spil"
Edit: Someone posted this which says that sport should actually be "et spil" (such as football and rugby and other similar ball sports), where as "lege" is more to do with playing with your imagination (such as with toys or Lego)