I just found out that there is an entire American Dad! episode that parodies Labyrinth! I watched it and it was amazing, easily one of my favorite episodes of the entire series. While they certainly did differ from the source material at times, it contained many references that fans of the movie such as myself will instantly recognize. A prime example of this being how Avery Bullock was dressed like Jareth the Goblin King.
After hearing that Gravity Falls wanted to do a Labyrinth parody but couldn't because their target audience wouldn't understand the references, I remember being very upset and disappointed. American Dad! however is the perfect show to parody that movie, with a majority of the viewers being adults who grew up in the 80s and would've seen it when they were kids.
There is one thing I'd like to warn you about before you look up this episode and watch it though. The unrelated subplot with Roger is disgusting! I'm not even going to say what it is. It's not NSFW or anything like that but simply too gross for me to even justify mentioning! It is easily the nastiest thing the show has done so far. Being unaware that such a sickening subplot was in the episode, I watched it after eating and it's an absolute miracle that I didn't throw up! I don't know how I managed that. If you have a weak stomach, I recommend either fast forwarding through those parts or avoiding the episode all together. Unfortunately not even an awesome Labyrinth homage is worth exposing yourself to that level of shock humor.
Aside from that, it was one of my favorite episodes by far.