I've looked several times for that quote. Not sure who it was from, but there seems to be some wisdom in it.
It's similar to how one may find archery fun, and archery was designed to kill people, but people don't find archery fun because they want to kill people, they just find it fun to shoot arrows and that gaining of fun probably was designed to make people better at violence but there's no actual direct connection.
On the other hand, the gaming situations where I have seen the negative aspects of nature come out were games that layered social aspects on top. MMORPG's, especially ones like DayZ, and, at worst, competitive games like League of Legends. When a single player game gets bad, like Doom or Nox, it gets bad over the multiplayer aspect. That's where all the nasty stuff really comes out, and it's not the art or the violence in the design of the game itself causing it, but the socializing aspect, power imbalances, etc. Meanwhile, people are cooperating pretty well in games like KSP or Minecraft as long as you avoid PvP servers, and even in the really dark, violent games like Dark Souls, again, as long as you stay away from PvP.
Human violence instincts seem to come out in situations that simulate social pressures, such as those where there is evaluation, power imbalance, and competitions. Single player games, no matter how much blood is falling on the floor, don't seem to do that to their communities as long as PvP is not involved.
To put it another way, if throwing feces was common behavior among humans, you might say "this isn't a human problem, it's a primate problem." And you'd be right, in a sense. But the key point is that throwing feces (as well as violence) is more easily avoided behavior for humans than for chimps. A human might choose to yell to express a level of anger than chimps only express with feces throwing (I might be uninformed about the feces-throwing behaviors of chimps, but you get the point). When we fail to take advantage of opportunities to avoid violence, we should ask ourselves why.
That is, I agree it is not an excuse to say "animals do it." But, it is also somewhat askew to me to have a barrier to our explanations that do not involve "humans are just animals."
It's not my intention to suggest that enjoying those means that our socialization has failed or that we are dangerous (which I do not believe), but that those games and movies appeal to something in our nature that still exists in many of the most well socialized Americans.