Consider a band that wants to hold a concert at that park. They would need a permit, which obligates them in certain ways to the city. Such permits are pretty universal and for good reasons.
But now, a company far away can easily appropriate that park for their own uses with no permit at all. The result might be a very large crowd (just like with the concert) making heavy use of the park, interfering with local's use of said park, and if something bad happens, no liability for the 'organizers.'
In an ideal world, Pokemon Go would not be a problem, nor would concerts. But that's not how it really is. Large crowds of like-minded people suddenly appearing at the local park are at the very least quite intimidating, and potentially scary too if that crowd's mood turns ugly for any reason. This is why some are viewing the phenomenon as a threat. At least with permits there is some oversight.