It's quite an interesting question. There are lots of privately owned 'public' spaces in meatspace, and the function of a space (a place where people get together in public) and its ownership (municipal, commons, private) don't always overlap.
Which doesn't necessarily mean that Twitter should be treated as a town square, because it's clearly something different to that. Similar sorts of concerns about the centrality of private spaces to public use led to PruneYard Shopping Center v. Robins, a California case allowing political activity at shopping centres against the wishes of the operator. That case hasn't been widely followed in other states and countries, though, probably for good reasons.
Which doesn't necessarily mean that Twitter should be treated as a town square, because it's clearly something different to that. Similar sorts of concerns about the centrality of private spaces to public use led to PruneYard Shopping Center v. Robins, a California case allowing political activity at shopping centres against the wishes of the operator. That case hasn't been widely followed in other states and countries, though, probably for good reasons.