God damn, I knew I'd have to explain this a million times.
Parallel Works is an official Gurren-Lagann project animated by Gainax. It is a series of music videos using the soundtrack of the TV series. Each one is directed by a different director. They don't have to make any canon sense, they just have to be based on Gurren-Lagann. They can be about whatever each director wants them to be about.
I'm gonna copypasta that every time someone asks.