They've been a recruiting rival a lot longer than they've been a conference rival. Before they joined the conference they had a winning record against OSU, 4-2. As a major power in a neighboring state, I would've called them a little bit of a rival in that two decades plus.
But they became more of a rival when they joined the conference in 1993, obviously. If you don't understand that all members of a conference are rivals by definition then I can't help you.
Almost all rivalries are geographic. Do you remember the Big 33 game? It's not just an Ohio State-Penn State rivalry, it's an Ohio-Pennsylvania rivalry. There's a regional culture element to it too.
I'd be more interested in discussing the nature of rivalries, the great historic rivalries, how they evolve over time, how conference expansion affects them, etc., than just shouting "We only have one rival! They're not Michigan! Don't tell me they're our rival!" I'm actually looking for an adult conversation but it seems I'm alone.
That's okay. I was alone when I said OSU and Michigan had to be in the same division or it would kill the rivalry, and I was alone when I said Everett Withers was the problem in 2012-2013 when the rest of Buckeye Nation wanted to fire Fickell. I was also right when I said Thad Matta's second-to-last Buckeye team wasn't good enough to deserve an NCAA Tournament bid and this board banned me for saying so.