In no sense is the Balrog a dragon, either. It's a demon of fire and shadow. Dragons are "worms", ie, snakes: they have to be reptilian to qualify as "dragons" in all but the very loosest usage of the word.
The reviewer was just confused, because in the scenes where they fall, you can see the fire and wings of the Balrog, but not much of the body. It does look a bit dragon-ish, if you forget what it looked like standing on the bridge.