As far as the business of reddit is concerned it provides the tech to run communities on, reddit itself doesn't manage the communities themselves (with the exception of admins stepping in to remove illegal stuff I suppose).
In your analogy reddit is the property owner or landlord of the community center, but it does not operate the community center, so volunteers are necessary.
I've volunteered at all sorts of community centers, schools, etc... Never once at a for-profit business in town.
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