Of course it's private property. It's not a government owned park or a road or something. It's a shop owned by a commercial company. It's private no matter the time of day. That they let people access their premises does not make it a public property. If you were to not follow their rules and a staff would tresspass you, you'd have no business remaining on their premises. Because it's private property. Their property, their rules. You have no rights or entitlements to anything there.