First, I agree with OP. Classless and beneath the office.
I also think things like this are classless - and it's not an anomaly. This is basically the show format - to disparage Trump's mental health.
Now, the criticism can be made - why stoop to the level of these two predictable and unimportant dorks? Not sure I see the value in that, but it may be fascinating to return to this thread in a few months and see where this actually goes. As with a lot of Trumpisms, this may make a lot more sense in hindsight. May not. But it'll be interesting.
A couple of contextual thoughts:
1. There is and has been a clear media war between Trump and CNN, MSNBC/NBC (and others, but mostly these) since day one. We are talking about a guy that may have run for president as a personal FU to Obama after being embarrassed at a dinner. After the week CNN is having, who can say they will survive a Trump term, let alone two Trump terms? I think he sees them on the ropes and wants to drag MSNBC into the discussion, maybe pick up a two-fer. There's never been such a nakedly anti-administration media push as there has been this time. Ever. A couple of guys will cite something they think was exactly the same for Obama, but a google search of Trump Russia will destroy any argument. It buries birther stuff by millions of search results. Trump has to stay on the offensive here. Has to. If he fails to do that, it will take the foot off the neck of the media corporations trying to bury him, and that would be foolish. So, even though it's cringeworthy today, it may in hindsight prove to be savvy er.... lucky depending on where it goes. Just a thought. This isn't Ronald Reagan's Whitehouse where the MSM had a monopoly and cared about the appearance of journalistic integrity. No network cares about that anymore, and especially Trump better stay on the offensive, and if you don't like Hillary Clinton's politics, you better hope he does too.
2. Speaking of not Reagan - Trump is a Boorish, classless, asshole. This isn't news, fake or otherwise. I didn't vote for him to be a sunday school teacher. I voted for him to 1. not be Hillary, 2. appoint Constitutionalist judges, 3. wreak havoc on the swamp. MSNBC and CNN are major swamp players. Holding their lack of professionalism up to the light is a very good thing. I wish it didn't have to come from the office of the President because it is unseemly and cringe-worthy. But if not him, who?