It's really simple, I believe they serve up their videos with Flash which your tablet doesn't support. Flash for video isn't going away yet in many cases because HTML 5 video is still lacking all of the security features sites like this one require. So they did the next best thing, they built a custom app for your platform which gave them the security they desired and you a full user experience.
Edit: Just confirmed I can watch their videos on my Android tablet, thus it's just a lack of Flash that caused this. In fact on my ASUS Slider they are playing perfectly.
They do. The BBC use it for the web-based version of the iPlayer, for example. (which only works on iOS devices and various set-top boxes and web-connected TVs - try it in the iOS Simulator or any other desktop browser with a spoofed user agent and it'll fail)
Basically, the (HTTPS) server can require the client to provide a special Apple-signed client certificate, which the server then verifies. If verification fails, it closes the connection. If it succeeds, the video is transmitted encrypted (SSL) and plays back just like any other <video> tag.
There's also a variant that lets you statically encrypt the video and serve it via Apple's "HTTP Live Streaming" protocol, with the keys for decryption downloaded via the client-certificate-authenticated SSL connection described above. This lets you avoid the overhead of SSL for gigs and gigs of data, as you only have to encrypt the files once, offline.
It's not even like these are major motion pictures. They are clips from a television news program that are released for free over the air and have an effective shelf life of less than two weeks. The potential downside to posting their videos in iPad compatible h.264 seems minuscule.
Android has dropped Flash, too, for anything beyond ICS.
So has Microsoft for the new Metro browser.
So has Adobe, for that matter, if you read between the lines (yeah, they've only "officially" dropped mobile Flash, but desktop Flash is on deathwatch).
A year from now neither any new mobile device nor the default browser on desktop Windows will have Flash.
Edit: Just confirmed I can watch their videos on my Android tablet, thus it's just a lack of Flash that caused this. In fact on my ASUS Slider they are playing perfectly.