I didn't work on the server end of things, but I recall hearing at work that normal Internet streaming doesn't work because the general assumptions made about connections are violated.
The latency is long, and connection pathways change often and by extreme amounts. A normal web-app will detect a problem and reset the connection. The software I worked on needed the client end "adjusted" to work.
The official NASA communications uses a special network whose name I don't recall (a bunch of letters). Internet access uses a totally different "be nice if..." system plugged into consumer Internet.
The computers inside the Space Network cannot access Internet servers. They can use an airgapped proxy in Houston (connected by HDMI cable only so the Internet PC seems to be a camera on the Space PC), so they could in principle browse anything and use the “special” remote desktop video (explained above) to view it; but that requires a helper in Houston to do the actual typing for you, and for viewing streaming video it would be pretty lousy if it wasn’t aware of the final leg in a seamless system. Watch a video on a remote desktop over a horrible laggy connection to get the feel for it.
So what do you do about watching video with a bad connection? Download the file first and watch (eventually) when you know you got it all; or use lots of buffering. It seems that most watching apps are doing away with expected buffering; e.g. pausing for a while doesn't make it buffer the whole movie: and is unfriendly to poor or intermittent connections.
Game of Thrones is on DVD, so maybe he's not streaming at all.
Update: see this press release.