This absolutely does not violate the EU's guarantee of freedom of movement for citizens. You're conflating your intuition about how that works ("as an EU citizen i have the right to access any and all public spaces without restriction") with what it actually means (EU member states must treat citizens of other EU member states the same way they treat their own citizens wrt entrance, access to employment, taxation and access to government services).

I think, like you, that what they're doing sucks. I think it sucks less than the alternative, which is that the city become nearly uninhabitable to long term residents due to the tourism crush. But this absolutely isn't a freedom of movement issue and to call it one makes you sound like Americans who think that getting banned from Facebook violates their free speech.