Not ruling out that they played some instruments on it, but since it doesn't seem that they wrote it, I don't see why they shouldn't demoed it.
They were good friends and it was probably a friendly favour in terms of appearing in the video. Didn't Jon and Richie appear in a Cinderella video in the 80's as well?

And they didn't cover House of Fire, they demoed but didn't use it for New Jersey and then the song got passed on to Alice Cooper who released it.

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