Is there another word, better than 'level', that you would prefer to use to describe the difference between a game in which you gain power/abilities piecemeal, versus one where you achieve that in chunks with numbers/labels attached to them?
EDIT: I understand that in theory the distinction could have no relevance to gameplay, because a highly granular progression could still be based on levels. But in practice that would mean a lot of levels. So in general the distinction between leveling and non-leveling games tends to be a difference in power curves.