While the involvement of ICE is a bit bizarre, legally speaking most of this is par the course.
Most theatres state up front that you cannot bring cameras inside - if you are found to have a camera, you may be asked to leave.
Additionally, the illegal recording of a film is technically a felony, and in pretty much every jurisdiction if a Law Enforcement Officer (and in many places even just an ordinary citizen) has - EDIT probable cause /EDIT - that a felony is being commited or is about to take place, they are empowered to make an arrest. Thus, given that the man was wearing an identifiable recording device into a movie theatre, his detention and questioning are at least legally defensible.
Personal disclosure: I do not support the MPAA, I am an advocate of free culture and media, and I personally feel that the laws as they stand are unjust - a felony is an absurdly harsh punishment completely out of proportion with the alleged "crime". It might have been somewhat more defensible twenty or thirty years ago, when bootleg video tapes were a thriving business, but modern "piracy" doesn't exist for the purpose of profit.