Triple H's Entrance Theme

I recently came into a copy of the WWE Anthology. On the (otherwise weak) disc three, there's a track listing for 'The Game', which I'd assumed would be the Motorhead track. Instead, it was something I'd never heard before. Musically, it was much more of a takeoff on "My Time", with the sirens(?) at the beginning and throughout, and a riff that deviates from that track less than 'The Game' ultimately would. The lyrics, however, are more reminiscent of 'The Game', sung by someone completely different (not Chris Warren). It almost plays like an early demo of 'The Game' that would have been tracked before Lemmy/Motorhead came on board.

Did he ever use this on television? This whole set had a few minor deviations from the themes I was used to, but I feel like this was the most noticeable of the lot.