I don't think it is obvious that he is wrong. Previously the property had a parking lot, where people could pay to park and then go to the beach. This parking lot was not profitable, so he decided to close it down. There is still public beach access, just not through that parking lot.

I think there is a reasonable argument to be made that he should provide access through the road to the parking lot, and just disallow parking, but it doesn't seem obvious to me. The previous owner did not allow free access (there was a gate), so I think it is OK for the new owner to forbid access entirely.