Regardless of what you think of what rights a private business should have, what's going on in that photo is blatantly illegal. It's been 15 years since I last did security but unless things have changed dramatically that security guard can't do that. Security guards have no special powers that an ordinary person doesn't have. You're there to "establish a presence" and "observe and report".

Even stopping a shoplifter is almost impossible. In order to legally be allowed to conduct a citizen's arrest you need to see them take the item off the shelf, follow them throughout the rest of their shopping trip, never losing sight of them, and then wait from them to actually leave the building before you can theoretically try to stop them. If you ever lose sight of them then "theoretically" they might have put the item on the nearby shelf and you just didn't see it. Conducting an unlawful citizen's arrest can land you in jail so no one ever bothered risking it.

In cases where someone did something that was against the business rules we were told to confront the person and tell them to leave. If they refused we were to call the police and report the incident. Don't ever put your hands on the person or else you risk assault charges.

On an unrelated note. If you ever go to a concert and a security guard searches your bag and confiscates your drugs, you should know that the security guard did in fact take it home with them and smoke it. This happened all the time. We had no more legal right to be in possession of those drugs then you did.

It's not private property, read anything regarding business licenses. You CANNOT discriminate against customers and randomly declare they are trespassing, almost all trespassing charges are because the person is committing an actual crime, like breaking in while the business is closed. You can SUE the business owners for forcing you to leave and the cops if they ticket you, as it is NOT trespassing, it's discrimination.