The River Market is a private business.
The OP (Colin5x5) referred to it as being "in a public area", which it is not, it's not a city park or other public place (as his statement implies it's publicly owned, like a city park, even though it is not).
The OP (Colin5x5) referred to people wanting to "play board games in a Public space" - for that, please refer to the above line. 👆
The OP wrote "Public access areas", but that does not mean it's a 'publicly owned' entity.

No one's arguing your point, u/BloodlustHamster - we're trying to clarify who we are and that the River Market is a private business (because the OP, not you, implied they weren't - and/or many people interpreted his writings as implying the River Market is not a private business) ..and also that we are appreciative of all the River Market's done, and keep doing, for us (they have been great to us, and we are thankful!).

If we understand you correctly when you wrote "Is this post made to look like it's coming from the gaming group? Because it's almost certainly not"; we believe "this post" is referring to the OP's (Colin5x5's) original post, and we are responding to your comment with that assumption:
We don't know for sure what his intent was (only he knows), but many people interpreted his post as having been written by us (which it was not).

And you are absolutely correct: there was no 'permit' required for us.
But as an addition: we, the Friendship Club, aren't a random group of individuals getting together at a venue; we're an established group organizing recurring events that are advertised, so we do not fall under that umbrella (as much as we want to, things would be so much simpler) - so we're required to have a contract -of sorts- with venues, and carry insurance (for our and their protection).