The uniqueness of human beings is an issue at least as old as Aristotle and has at least two components: First, Aristotle places our unique status as the primary way of understanding both our purpose and our goodness. The Greeks thought that everything has a purpose, and that the purpose of anything had to be unique. Following that, if we think that we are not unique, we would start to think there is no purpose in our life, no function we are supposed to fulfill. And since the good knife is one that fulfills its function well, the good person is one fulfills our purpose well. If we have no purpose, what happens to our notion of living well?
What, then, is unique to humans? What is our purpose? Many people have thought of different answers, and for a long time, it always struck me as odd to even ask. Some people point to our thumbs as being unique, some to the creation of culture (non-biologically driven patterns of learned behavior), some to language, some to thought, some to reason. Each of these, 'cept the thumb, have been shown not to be unique, and a thumb is not much to hang your hat on. OK, you could hang an actual hat on a thumb, but not a metaphorical one.
The reason this always struck me as odd is simple: its rather obvious that we are unique, that even if a chimp can learn language and reason, we are not the same as a chimp. In other words, our definition in terms of these features is so inadequate that it seems silly to ask: what makes us human? And without the Aristotelian background, the importance of the question escaped me. So what if monkeys can speak, or reason, or have a culture, or if we discover some other species with a thumb? Why would that effect our conception of ourselves? Why would that threaten our conception of ourselves as unique? What rides on determining unique features of the human being?
Now when we discover that some feature that we thought was unique turns out to be shared (The bonobo is able to grasp language at a high level, chimps are able to reason, some chimps have a culture, some chimps use tools, etc., etc.) the obvious response is mere passing interest. "I thought that feature was unique... oh well, I guess it isnt." I have had that reaction myself and I see it in others. So where would existential angst come from?
Second (there has to be a second, there was a first... forgot? first paragraph), moral notions are limited (historically, if not philosophically), to people. This is not a Western idea. So, for example, the Comanche called themselves "The people" (Nermernuh). Everyone else is not. If you are of the people, you are protected by the people. There was, apparently, almost no violence within the tribe, or against anyone who culturally acted like a tribe member. However, anyone outside the tribe was not similarly protected. They may trade with you, or they may kill you, that choice is up to an individual Comanche, and simply not part of their ethical framework, not subject to judgment. Other people's moral status was like any other piece of nature, sometimes to be preserved, sometimes to be used and sometimes to be abused. It has been argued (I think correctly) that the whole 10 commandments were originally understood in the same way: "Thou shalt not kill" really meant "Thou shall not kill a fellow Jew." It, too, was a tribal notion.
The question then of what a human being is connects to our conception of morality: humans are beings to which we have a moral duty, while non-humans are not protected by moral codes. It is also easy to see how correctly defining the human in terms that shape our moral attitudes (reason, not thumbs) is one way of intuitively increasing beings with moral rights. "I know those things do not act like us, but they really are human, and hence we have moral duties towards them." "I know we do not seem to be human to you, but we have this uniquely human feature, too, so you should treat us as moral agents." Historically, when we have broadened our notion of the human, we bring more people into society, and start acting better. A good definition of a human, then, has been of great importance. It is then easy to see that if we are not so important, not so unique, nature gets raised by default. Many people who do not see humans as unique see us as part of nature, thus raising the moral status of nature. We call them "environmentalists."
So now we can see why much of the artificial intelligence science fiction asks whether or not computers that develop consciousness are moral agents. Early in Star Trek, The Next Generation, we see a trial to determine whether or not Data, a computer, is a moral agent, or not. Is he an officer in the Federation, or is he like any other computer, to be used by its owner as its owner sees fit?
I think our angst about thinking computers is not existential, but about control. It is the worry of Mickey Mouse in Fantasia, HAL in 2001, and Cyberdyne Systems Model 101 Terminator.