So the security guard was wrong.
Operative phrase "provided it does not impose itself on others or take away from the overall shopping experience.”
If they mall, being private property, has in place a policy of not allowing something - ANYTHING - then they have the right to remove person or persons acting against that policy.
The issue is private property rights - not prayer, not firearms, not right nor wrong.
If you are on someone else's property and you go against their wishes, they have the right to ask you to leave.
If I came to your house, and did something you found objectionable, or caused a disruption to you, and then claimed I had a "right" to do it, you'd be rightly pissed and call the police.
It's the same thing. I'm not understanding why you're having difficulty with this basic concept.
Unless you just feel like arguing; in which case, have a nice day!