I think they have to charge in this case. Because unlike Spectrum, it isn't your land you are using, it's "Arte" land. And if it was free parking, then cheap people would be parking there on gamedays. Of course the other way would be for them to lease the land on non-gamedays, and provide free parking. But I don't know how well that would fly with those financing the project.
Personally, I think they if they want to build a big structure, they should provide their own parking. But it sounds like they want to cheap out and slowly nibble away at the current lot.