There is nothing preventing other animals from becoming just as good at manipulating their environments, though. Raccoons have independently evolved dextrous hands very similar to those of primates, for example.
Yes, there are a few other species with dexterous hands or other organs (such as tentacles) that I suppose could have the potential to evolve in this way. I just think it was most likely to be a primate as they are by far the most common type of animal with dexterous hands.
The point I was making was that a species is far, far more likely to develop a complex toolmaking ability if it comes "ready made" to do so. Our ancestors could still use their hands for the original primary survival purpose of picking fruit, etc, while they gradually developed the use of tools. Whereas almost all other species would have to make a massive physiological transition to develop any kind of dexterous organ. And of course every stage of that transition would have to be advantageous.
Also, of course, it requires other factors such as whether or not the whole physiology of the particular species, not just it's dexterous organ, is appropriately adapted to make good use of tools (e.g. a throwing arm) and whether or not it's environment lends itself to the use of tools.
I'm sure you've seen people on TV without working arms who've impressed with the intricate tasks they can accomplish using mouths and or feet. These are people born into a species which normally relies on their hands, and yet they're capable of learning, with practice, to do many of the same things without. In a species which never relied on hands, there's no reason they couldn't manage to accomplish complex tasks of tool-making and tool use.
Sure, some people can develop a few amazing skills without their hands, but generally they are still very limited. In the natural world if you don't come with a physiology that is "ready made" to make tools, it will take so long to make or use anything useful, that the time and effort would be a hinderance and provide no advantage. There would therefore be no evolution in that direction.