They can. They're not under a gag order but I don't think any other show can play clips of Howard's show.
That's because Howard owns his show as part of his deal with Sirius. He believes that he can make money off of syndication (read: repeating old shows) in an era where everyone else gives their show away, in a medium that's habitual, for content that's extremely dated, guests that are no longer relevant, "current" events discussed that people either don't remember or have information that's changed since that particular interview and after he's proven that the main draw of that show (his ability to relate to his audience) is a complete fraud.
They played a clip of the View, not Howard's show.
That clip is older than dirt though. This happened way before the merger, probably 2006.
After the merger they played clips from Howard a few times and then after that they were told they could not play clips from Howard. Same goes for Jay Thomas, he has said he can't play clips from Howard's show.