I'd say that the Lady Gaga video's main influence is fetish-fascism and a desperate attempt to try and look original while still closely following a standardised pop-video style laid down by Cher and Madonna.
While 40k imagery does share some elements with fetish-fascism (uniforms, deformity, ect) I think it's a bit of a stretch to say the video has any distinctly 40k elements, it could just as easily be compared to Mutant Chronicles, Command and Conquer, Marilyn Manson's “burlesque” phase or the Street Fighter Movie.
^
of course!
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~The ravings of a single mad Goblin is bad enough, but such a power-hungry, malice-filled creature as Mortis can never hope to be understood~