Are you asking if it's permitted to drive around the campground? That would entirely depend on the campground's policies. Legally, a scooter of that size is a motorcycle, and generally can go anywhere a motorcycle is permitted to go.
I would think that some campgrounds might take a dim view of taking a motorcycle on what are mostly pedestrian walkways, even if they allow golf carts or bicycles on them. I don't think I've seen many people driving toads to campground pools or shower houses, but that may just be the campgrounds I've stayed at rather than a general rule.
(Even though I recognize that there are great differences in visibility to other drivers, I find it a bit amusing how many posters are worried about a scooter's ability to maintain speed going up hills or around tight corners. There are plenty of hills that my class C cannot maintain the speed limit going up, and I don't feel that it's unsafe for that reason.)