It being on a closing document doesn't mean it is not a rental expense. That is not an exhaustive list of closing costs, just examples of them. It is one of 3 things, a deductible HOA expense, part of the cost basis, or non-deductible social club dues.
In this case I would have added it to the cost basis of the property, given it was mandatory and of no benefit to yourself. This charge is also more traditionally called an initiation fee, which is how I'd argue it to an agent or the court.
