it's been a while since i've dealt with cities and zoning, but i don't believe merely zoning land for X immediately makes it X. In fact, often it's been my experience that it's the other way around. We have lots of empty land that is 'zoned' for multifamily living (i.e. apartments). But there are no apartments there (and often there might be homes on the property). It's not that the home is in violation, it's that the zoning came after the house and is part of 'the larger picture'. When things were zoned those folks had the chance to protest the zoning but might not have, banking on things being more valuable in a college town later. But if redevelopment occurs then it would have to comply the with zoning overlay going forward.
And often you can build things like churches (and probably parks) in areas zoned for lots of different uses.
But even zoning it for a park (which might actually be 'green space' or something 'outdoor' not actually 'city park') likely wouldn't change the ownership issues. And the land owner could always file for a rezoning since those things aren't set in stone.
I don't believe a city could simply 'zone' a dilapidated property as a park to force the teardown of a structure or anything like that.
Yeah, I didn't mean that zoning would settle it, just that it is an example of one aspect that could be used to build a case that the city intended the area to be a park, recreation area or fairground, because the law is silent about actual ownership of the land in this instance. Zoning, the terms and conditions of the lease/land transfer, makeup of the organization that runs it etc...can all come into play once this ends up in the legal arena, which hopefully it will.