<sigh> The violence being (A) professional wrestling (and if you believe that is real you are going to hate what I have to tell you about the Easter Bunny) and (B) against the CNN logo.
There are plenty of opportunities to hate and criticize Trump without looking like a total idiot.
I also really struggle to see the original gif as being particularly shocking. In fact I thought the Kathy Griffin thing was worse (at least, it was just very very odd, not really sure what point it was supposed to be making). Again, for me, the thing about Trump posting the image is just how juvenile it makes him look, and lacking in the dignity a president ought to have. It's just a bizarre thing for someone in such a position to do.
But the defence for CNN, I think, is that it turned out the other stuff the meme-maker had posted really was vile. Having found he was posting such stuff, I can see they might have felt morally obliged to ask him to stop doing so. I'm just not sure why they decided to go to all the trouble of finding the guy in the first place. Is it because the CNN guys don't realise how commonplace such stupid memes are?