I’m glad you asked that question.
The crucial difference is that there are private properties which have restricted access and Single Family Private Residential Property (SFPRP).
Those extra words are critical. SFPRP is not allowed as any game play may directly impact on someone home which would be very intrusive to that individual/ single family where they should expect privacy. This is why applying that rule is enforced as described in this clarification
If it is a multi-family building such as an apartment block then the communal space is fine as that is shared. So in apartment complexes where there are shared facilities a play area that only a few can use is fine.
This principle then carries forward to more general privately owned property. If it’s not someone’s home and some people can access it even if the range of people is very limited then that is ok.
So although a space like a university is private, with restricted access it is fine as it is not someone’s home.