Well it does meet the definition of a private good (excludable, rivalrous.) Maybe it should be treated like all other private goods and rationed by price. I guess in theory the money can be given to poor (if it's done by the city which owns the parking spots.)

I'm not saying that it's the best solution, but it does seem arbitrary to have some private goods rationed by price and others rationed by lottery. Just because "that's the way it's always been". In any case this app or rather the people using it don't rightfully own the parking spaces, but they are taking advantage of a market inefficiency.