Did Gorbachev say that his intention was to destroy Communism?

There are several questions in here. I'll try to address each one:

Q1: Did Gorbachev betray his voters who voted for a return to Leninist ideals?

No. The reason he didn't do that is twofold.

1. He didn't have any voters. Gorbachev came to power in a totalitarian dictatorship. His assumption to power was completely undemocratic. Nobody hence voted for any return to Leninist ideals. (There was an election in 1989, and this election served both to legitimize Gorbachev and take steps towards democracy, but it did not bring him to power, and the election would not have been able to bring him down from power either).

2. A "return to Leninist ideals" means primarily things like equality, and the people being in control. This means democracy, and this was what Gorbachev was working for. His aim was a socialist democracy. He believed in Marx and Lenin's ideals, but he had realized that the so called "dictatorship of the proletariat" was not the way forward. Hence he retained the ideals, but rejected the methods. Therefore it was not a betrayal of the ideals.

There therefore was no voters to betray, and he also did not betray his supporters or Leninist ideals. What he did was simply to fail. Instead of succeeding in his aim to bring democracy to the Soviet Union, his steps towards democracy instead led the Soviet Union to collapse. To his credit though, this has led to democracy in Estonia, Lithuania and Latvia, so his efforts wasn't a complete failure.

Q2: Is the sources for the text reliable?

No. Felix Goldberg in his answer explains well why it isn't reliable. In fact the claimed sources generally don't seem to exist. Also in one case it's claimed to be a speech, in another an interview, which casts further doubt on the text.

There is today a publication in Slovakia called "Usvit" but it's doubtful it existed in 1999, and if it did it's a one-man show by a local fringe politician. It seems highly unlikely that this guy had secured an interview with Gorbachev.

The text is variously claimed to be from the American University in Turkey. That University does not exist. There is an American University in Cyprus, though. However, the text is otherwise claimed to be from an interview in Ankara. The only reference I can find to Gorbachev and Ankara is from a 1997 publication in Turkish. The source is not reliable.

Q3: Did Gorbachev say that his intention was to destroy Communism?

No. I can't find any reliable sources on Gorbachev himself saying that he wanted to destroy communism. The text in this question seems to be the only case, and as we have seen, these texts are not reliable.

During the cold war, the word "communism" was generally associated with socialist dictatorships, while the word "socialism" was wider and included those who wanted both socialism and democracy. With that usage of the word it could therefore be claimed that he indeed wanted to destroy communism, as he wanted to make the USSR democratic. But he himself seems not to have made such a claim.

Q4: Is the text authentic?

No. Most of the things in the interview seem rather unremarkable. Gorbachev claims to want a social democracy, something he has said otherwise. He said even before the fall of USSR that he wanted a more open market. There is no mention of a conspiracy at all, that seems to be Anixx own invention.

In fact, the only remarkable statement is "The purpose of my life was the destruction of communism, unbearable dictatorship over the people". Nowhere else do we find Gorbachev claiming that he wanted to destroy communism.

We do however find him saying that he wanted democracy. As such this quote is probably an intentional distortion of what he said. He most likely said that he wanted to destroy the unbearable dictatorship over the people.

So whoever decided to wrote the original article was probably a dedicated anti-democratic communist, and decided to change the headline to something more controversial. Therefore, at a minimum we can conclude that the article as a whole isn't reliable, and that the claim that he wanted to destroy communism probably is falsified.

As the sources seem to made up, and also Gorbachev's visit to Turkey seems made up, it's likely that the whole text is made up. But it's probably largely made up from things he actually have said in other interviews and in his 1995 autobiography. The claim that he wanted to destroy communism is however most likely completely invented.

I trust David Remnick's Lenins's Tomb: The Last Days of the Soviet Empire as a source, which includes this passage:

To begin with, Gorbachev himself was still convinced of what he called the "rightness of socialist choice." He continued to see Lenin as his guiding intellectual and historical model. There is absolutely no evidence to suggest that Gorbachev was out to undermine, much less destroy, the basic tenets of ideology or statehood of the Soviet Union. Certainly not in 1987.

It may be relevant that 1987 is closer in time to the main transformative events affecting Soviet Communism than is 1999. I personally don't think the quoted "admission" is authentic in an objective sense.