I wouldn't call it a "rhythm game" because it's virtually a side (down) scroller that has you strumming randomly to achieve points, not based upon the "rhythm" of the actual guitar that you do your best to poorly emulate.
Calling it a "party game" seems fitting as the only person I can see playing the game during its heyday were college kids who would spend hours wasting their brain cells with a mix of liquor and the thrashing of a plastic guitar in an attempt to impress the walking Petri dish who would join them for their "brotherly" functions of the fraternity. I find it only fitting that now you see it in common arcade places and the only persons who will spend the $2 per set are the children trying to imitate their big brother Jack who is still working on his 2nd year, 5 years into his college tenure.
However, your confession as this being a game does a MASSIVE amount to explain that list of songs you sent me a while back. I often wondered where you'd pull out a brilliant song like "Paint it Black" to slap in the middle of the list while leaving out "Sympathy for the Devil" or "Can't you hear me knocking" off the list.