As a daft Brit, I think it's hilarious!
But you probably need to know the story behing the video, and also something of British culture to get the joke.
The song was re-released as a charity record, with one of the UK's top comedians (Peter Kay) miming to Tony Christie, while walking with various other UK celebs. You can see the original here, if you really want!!
http://www.captiveimage.us/Gallery/Musi ... iewer.html
It was number 1 in the UK charts for something like 7 weeks, so was obviously a huge hit. The army guys simply did their own parody of a parody - if you see the original, the army one makes (a little) more sense!!!!