No they don't.
This sort of anthropomorphising in popular science news stories really irritates me—especially when, as in this case, the anthropomorphising is being done by the scientist involved:
"When the keeper gave the orangutan the really nice food, understandably, that was the end of it," explained Professor Byrne [an evolutionary psychologist]. "But when the keeper pretended to fail to understand the original gesture and gave the wrong food, the orangutans stopped using the gestures they had used before and started using some different gestures," he explained. "And when the keeper half understood and gave the orangutan part of the treat, the orangutans started to repeat the same gestures that they had used, but they would repeat them even more enthusiastically."
Professor Byrne likened it to a game of charades. He said: "Part of the skill is to do the miming and the gesturing in the cleverest way - but also you are paying attention to what your team is guessing, and you tailor what you do next to what they are doing." Effectively, the orangutans were able to take into account the states of knowledge, ignorance and partial knowledge of the keeper and react, said Professor Byrne.
Setting aside the fact that the orangutans' behaviour is nothing like a game of charades, can anyone explain how this tells us anything about what is going on inside the minds of these great apes? In what way does their behaviour differ significantly from that of a dog that is being teased with a treat? If the dog begs in some way and you ignore it, it tries something else; if you give it some of the treat, it begs some more, getting more excited if you pretend to ignore it; if you then give it the remainder of the treat, it soon realises and stops begging.
I am pretty sceptical of evolutionary psychology as a whole. This sort of experiment simply bolsters my scepticism.