I thought their business model was like a gym: hope that most people won't use it. (Source: I have MoviePass and I'm seeing less than 1 movie per month because I'm too busy :-D)
Instead, this article claims it's:
1. Studio of movie $M pays MoviePass $X to market it to subscribers.
2. Subscribers see a movie they otherwise wouldn't pay for. MoviePass eats this cost ($Y).
3. Subscribers' word-of-mouth network effects bring in extra revenue $E that otherwise wouldn't have come in.
4. MoviePass stays alive if $E > $X > $Y.