As is the press. Outside of libel laws, the press is constitutionally exempt from any type of regulation. As impotent as the press is today, I wouldn't want any political party to be able to decide what it can and can't say.
I'm not advocating that they can't say whatever they want.. only that they can't call it news if outright falsehoods are being passed. The same way you can't market your product as beef unless it meets certain standards, or your Bitcoin company as a bank, and so on.
This is a labeling/marketing law, nothing more. You are not excempt from those by way of being a media organization. Certainly it is not a speech restriction. As a bonus, it would allow competitors to market on that label since now it actually means something.