No, I don't see they claiming that the use in games caused these deaths. What I think they are claiming is that it is necessary to protect the symbol such that when we see it, we know that we really are dealing with the Red Cross, not with some other random thing related to medicine. And that if the symbol becames banalized, this takes away the protection that the symbol should bring to them.
I understand this, but, perhaps in the long term they should consider using a more complex symbol, and including the Red Cross name in it. It is much more difficult to protect a symbol when it is so generic and simple to draw it.