If it was ANY USUAL mall I'd be more inclined to believe that, BUT they are assuming the "regular state duties" in a lot of ways. Remember the cases with the privately owned towns? This is pretty much that. The place is HUGE, with full time residents living inside of it, STATE PAID police/post office/etc. It feels like a private town to me.
Let's not get lost in the weeds here.
There is NO WAY that the current Supreme Court is going to consider the Mall of America as a company town or state actor. Not even close. The company town cases are fairly old and obscure, and the level of control exerted by the parent corporation was far, far beyond anything that Mall of America is engaging in.
The mall is simply private property, open to the public for commercial retail purposes. Can you really imagine that there are five justices who will say "Yeah, we think that the mall is essentially a state actor even though it's private property, and BLM has the right to disrupt commerce." Who would be that fifth vote? Kennedy?
No, as Loki stated, this will end badly for the protestors.