If everyone needs at least 5mbps* to stream, I reckon you need network switches and then I actually don't know how you create discrete wireless bandwidth for the passenger capacity of the larger aircraft.
First off, they're not likely to assume that everybody's bringing a 36" or larger HDTV on the flight. More likely, streaming bandwidth would be geared for a 7-10" tablet. Then in terms of file server capability, the easy out is to stream it "live" in the sense that the server is only having to put out a single stream of each movie; it means everybody's got to watch it more like a regular in-flight movie, all at the same time, but the file server itself isn't putting out a separate stream for each of x passengers, all at different points in each movie.
I'm not sure what the overall theoretical capability of a wireless AP is, but I'd guess it's possible to make one with quite a bit, or ISPs wouldn't be able to provide the service using relatively standard equipment. In the case of the plane, power is a non issue, since your entire market is sitting within a couple thousand square foot rectangle and inside a handy waveguide. As for interference due to so many clients in close proximity, I don't know how much of an issue that would be, but of course, using multiple APs on channels separated as widely as possible is also an option. I do know I've seen pretty dense offices running dozens of PCs on a single AP without any problems, and usually (depending on IT's whim-of-the-week) when there are separate networks by department, it's due to distance issues (and/or departments being territorial) rather than overloading an AP.
IMO, it should still be doable with less weight and bulk than an extra drink cart, I'm just not sure how much less.