Is there a possibility for there to be some form of sports besides Gladitorial combat?

Probably. I see Hunting being big among nobles. Given the amount of Couriers roaming the land in Skyrim, I'd say Track isn't out of the question either. Fencing probably. Maybe Horse competitions.

I would imagine "off-screen" so to speak, there would be running or swimming tournaments that some could participate in, exercises done by the military and some civilians, as well as basically just going out to take a walk. I'm not sure if there is a culture of ball games of any sort in Tamriel. Children probably play with balls, though.

I could see horse races being big.

I have another possibility, perhaps some of the games during the ancient greek olympics are present? Such as javelin throwing?