I find it interesting that the author of the BBC article is assuming that the male chimps are trading meat for sex. The original article goes on to state that female chimps don't hunt, so they can't obtain meat on their own. When the male chimps donate meat to the female chimps, they don't just get more sex, they also increase the chances that the female chimp will take in enough protein and calories to bear a healthy baby.
Humans look at the male chimp's giving the female chimp meat as "trading" meat for sex, but there are a lot of other constructions that could be put on that behavior. He could just as easily be trying to assure that his offspring will be healthy. Or trying to assure the health and well-being of a female that he's come to care about.
The original article says that people had tried to find meat-for-sex exchanges in chimps before and failed, because they didn't give the animals enough credit for long-term planning. They looked to see if Chimp A gave meat to Chimp B, then had sex with her two minutes later, and they didn't find that. The current researchers succeeded because they took a longer-term view and counted meat-giving and sexual activity over time. But it's possible that they're still not giving the animals enough credit -- what if the meat-giving isn't trading meat for sex but is something else entirely?
Observations of primate behavior will never tell us anything until we learn to just report what we see the animals doing, then think of every plausible reason why they might be doing that, rather than assuming that the animals aren't capable of doing what we do.