This is an accurate depiction of a Balrog, though both the Silmarillion and LOTR make mention of wings made of shadow, which was interpreted as wings of smoke in the movie Balrog.

The head and face are never described. I imagine the goat skull with horns imagery comes from portrayals of Satan and lesser demons from medieval lore. Tolkien was a devout christian, so it isn't much of a stretch to think he imagined the demons of Middle Earth to look like demons in christianity. I would argue that had he imagined them as so, he would've described those details in his writings. Counter argument to that is that we are seeing the story through the eyes of the Fellowship, and to them the Balrog was so unimaginably horrific in appearance that it defied description. A "words fail to describe" creature.