The amount of times played absolutely counts in how much of a rivalry you have. Rivalries take time to establish. What better way to correlate time with a rivalry than by showing how far back it goes or how many times it's been played?
I don't know how much ESPN will push it this weekend but they did post this earlier. And I saw Lou babbling about it a few days ago. I'm preemptively laying it out there that this "rivalry" doesn't mean shit. If Notre Dame wants to talk about a rivalry, they're better off pointing to USC.