okay guy who studied linguistics here, teaching a chimp to use hand signs is not the same as using language itself. just like you can teach a dog to understand spoken commands, they still aren't able to communicate via human language.
Is this because of intelligence limitations though, or simply physical limitations?
The reason you can't teach a dog to perform hand signs is probably not because the dog is too unintelligent to grasp the concept. The reason is probably because the dog lacks not only manipulative digits, but a large enough portion of their brain devoted to manipulating its paws to have that degree of dexterity.
You can however teach a dog to signal you by performing things it can do. Heck, my grandfather taught his dogs to smile, something that goes hugely against their natural emotion sharing context since among wild dogs, smiling indicates displeasure and not pleasure.
Likewise, the reason a chimp can't speak is likely more to do with the lack of ability to control it's voice box to a sufficient degree to produce the sounds necessary for language, as well a likely a lack of the physical tools in the mouth and throat to produce those sounds.
It's not at all clear to what extent chimps aren't using language itself. It's highly likely that they have natural limits to their speech forming intelligence, but I feel reasonable satisfied that they are using language with some degree of intentionality out of a desire to communicate simple ideas. Now, don't get me wrong, I think the limits of their speech forming intelligence are pretty darn harsh, as they don't ever seem to grasp the ability to ask questions in the way that, for example, Helen Keller eventually grasped in a profound manner when repeatedly signed to. Some instincts or processes necessary for high degrees of speech intelligence may be entirely missing. But I do think some rudimentary speech forming intelligence is present.