This is the silliest thing I've ever heard, and not every fictional red cross symbol is a threat anyway. This whole thing seems at least as ridiculous as the moral panic about violent video games in the early 2000s, except that I kind of expect ridiculous moral panics from conservative parents not so much from the official communications arm of one of the largest NGOs in the world. Absent any actual evidence I think we're just going to have to agree to disagree.
They're not calling for video games to be banned or even re-labeled, they're just trying to prevent the red cross from losing the intended meaning (which comes with an international treaty intended to protect aid workers)... it seems like the method of applying this mostly consists of asking nicely.