Empathy and not being empathic and sociopathy are different animals and this dualistic thinking is part of a problem of discussing empathy even remotely seriously
Being entirely unempathetic is sociopathy. There is of course a ton of middle ground in empathy, but the end result of promoting a lack of empathy would be promoting sociopathy.
If someone who never was raped and has no idea what rape is like uses it to describe just about anything that is not an actual rape, they normalize that usage, or that it is completely alright to do that with about any experience one can think of.
Of course we can imagine what rape is like to some degree. I think everyone who has heard or even read a story about something can imagine what it is like to be in that story. Imagine how dull every book or film would be if we were unable to imagine how the character feels or would react. No one who hasn't been raped has a full idea of what rape is like, that much is obvious, but most people can grasp the basics I imagine. As for normalizing the usage, I don't think that using rape in terms of a video game in any way changes the use of the word in other contexts. A rather remarkable feature of language is that words can have different meanings depending on context without hugely affecting it in other contexts.
Not only that leads to confusion, and ostracizing of actual victims, who are once again told to just suck it up, it is all humor.
I don't really buy into that. Humor often relies on taboo subjects, and that would not for one second take away my empathy for someone who actually went through it. Perhaps it is just me, but I have the ability to separate jokes and metaphors from true situations. In terms of jokes there's one I heard recently that goes something like how is a gay man like a tumbleweed? The answer is that it blows and blows until it gets stuck on a fence in Wyoming. Now this is a horribly offensive joke, but I'm gay(-ish) and it doesn't bother me in the least. Actually reading about the case that the joke is based on was really quite awful and disgusting, but I don't feel any less sorrow for that crime having read an off-colour joke about it.
And for populations already disadvantaged, and not taken seriously? That attitude can be -deadly-. Denied medical care, denied law enforcement help, denied access to other resources, focusing NGO workers in all the wrong directions, et cetera.
As I say, I don't think gay jokes truly have a negative impact on people. The idea that all jokes are rooted in someone's beliefs seems preposterous to me, and often I find jokes are the opposite of someone's beliefs. No one believes for a second that the person who was "raped" in Call of Duty has had anywhere near the kind of experience an actual rape victim has, nor do they believe that the actual crime of torturing a gay kid and leaving them to die is as funny as the humor in breaking the taboo around it. I think human being are generally not as utterly stupid as to see jokes and hyperbole and have it influence their views on the real issues.