Youtube'ing it:
[youtube]w5_EIikdFr8[/youtube]
Looks like a maple-necked humbucker-equipted strat. I don't know what he's playing through, but David Gilmour gets a similar tone by running a clean overdrive through a big muff (it was a ram's head style muff, IIRC.)
EDIT: of course, it could be that the guitarist is just miming playing guitar in front of pre-recorded music, although it sounds like the singer is live.
EDIT2: I never noticed it, but apparently every verse is the same music because only one verse was properly recorded:
[youtube]WcxMZTLSY4A[/youtube]
And now I want to hear William Shatner's version.