Your driving options will be limited in the park itself.
Reaching the camp is not a problem since you can drive around the park on the tar round, and have limited distance on gravel.
But the "4x4" routes in the park will be off limits. I would even not travel some of the open routes in a small sedan.
The road to tree top and the confluence lookout will be doable in a sedan.
I don't think you need a 4x4. But a high clearance more rugged type of vehicle is a definite plus in Mapungubwe. If you spend some money to get there, it may be worth spending the bit extra on a vehicle which will give you much better access to the park.
Nobody told that to my Clio
Seriously though, I travelled every 'open' road in that park with my small sedan and even a 4x4 road or two because of the non-existent signage. And there were quite a few other sedans around. I remember a fellow forumite being there at the same time in their Corolla.
Like Imberbe said it would be better with a high-clearance vehicle but it is not the end of the world if you don't have one. Big price differences in renting a normal sedan vs a SUV.
The road into the eastern side from the main entrance all the way past Leokwe & Treetop hide to the Confluence is sedan-friendly. So are the roads going further east from the gate towards Shroda dam.
The road into the western side up to the 2 camps and then on towards Maloutswa pan is also sedan-friendly.
Just take it slow and enjoy the scenery.