IMO, the definition of a "rivalry game" is one that everyone cares about regardless of what it means for the standings. It should still mean everything even if both teams are awful. Think Army-Navy.
The Florida game has obviously become the most important game on the schedule in the last two decades, but mostly because of how much it means in the standings. I don't know how much it would stand as a rivalry game on its own if, say, Georgia became a colossus in the division and UT and UF were both going 7-5 every year. This Kiffin-Meyer stuff has a chance to cause some real genuine hatred and push it over into real rivalry territory, but thus far I'm not sure it's there yet. The UT-UF game has always been played with an eye on the division title, not really because you just hated the other guy.
The Alabama game has always been mostly just about hating the other guy.