Obviously he can’t violate the laws, but as owner of a private company he has a very wide berth with what he can do. Not linking to a competitor is not violating anti-trust here.
I mean, that's the thing: He can. He just shouldn't. And he doesn't have enough people (or, most likely, anyone that he'll actually listen to) telling him what he shouldn't do.
No, he can't violate anti-trust (or any other) laws.