Perhaps the Balrog underestimated Gandalf, thinking it could cast him into the abyss, then fly back up to deal with the rest of the Fellowship. Alternatively, maybe it calculated that its best chance of defeating the wizard was to grapple with him at close quarters. Either way, the Balrog falling doesn't necessarily mean that it wasn't capable of flight.
Aren’t Balrogs just corrupted Maiar? I’ve never understood why it’s assumed that they all have to be the same. Presumably, they could have taken different forms, either by their own choice, by Morgoth’s, or just by the way the corruption took hold. Maybe some had wings and some didn’t?