[ashtonabc]

I have visited theatres that perfectly match your description in Taiwan, with the exception that the film has to be out on DVD. You choose the size of room you would like (some rooms are large enough for parties, some are comfortable for two), pay for the amount of time you would like to book the room (with discounts for longer amounts of time or late night bookings), and choose from their library of DVDs. You are shown to your room and the movie is played. There is a phone to call the front desk and you can order food and drinks to be brought to your room. The chain I visited a few times is called U2MTV [1].

[1] http://www.u2mtv.com/