Did the Chief of Soviet General Staff really say this?

I don't think that Marshal Nikolai Ogarkov ever wrote an autobiography, so we will probably never know his recollection of that conversation. However, the interview with Leslie H. Gelb was published while Ogarkov was still alive (he didn't die until January 1994), and the story was quite widely reported elsewhere.

The fact that the story was never challenged by Ogarkov probably means that the sense of the quote at least, if not the exact words, is correct.

It is a fact that Gelb reported Ogarkov as saying this. Gelb was working for the New York Times as their National Security correspondent at the time of the metting, so it would have been his job to report this accurately. It is of course still possible that Gelb was either lying, or misremembering. Ogarkov was still living to refute this in 1992 (although perhaps not reading the New York Times).

Here's another version, taken from an interview with Gelb archived here at George Washington University. I'm not sure of the interviewer or the date of the interview, but it was apparently added to the archive on February 28, 1999.

When I had gone back to the New York Times in 1981, I had a meeting in Moscow with Marshall Ogarkov, the chief of staff of the Soviet armed forces, one of the most brilliant and impressive people I had ever met in my life. He was able to combine strategy and military affairs and politics with technology and economics. He was truly a strategic thinker. And in my conversation with him, I was talking about Soviet military advantages in Europe, sort of the usual con-job we did on each other at the start of any conversation, talking about all the bad things that they were doing. And he said, "Les, cut this out, will you? You know you're ahead of us in Europe and in every other respect, and you know that America's lead on the Soviet Union is increasing, not decreasing. All modern military capability," he said, "is based on the computer, and you have weapon systems now based on computers that we're only beginning to have. I'm just beginning to install computers here in the Soviet Defense Ministry," he said. "You have little kids in America, three years old, who know how to deal with computers. It takes years here to train Soviet recruits in the military to use them, because they've never used them before. We're afraid of computers. If we start deploying computers, it's going to mean loss of political control for the Soviet leadership: it'll mean information can be spread without the okay of the central government, so we're afraid of that; it puts us at a major strategic disadvantage with the United States. And unless we change that situation, we're going to fall irretrievably behind America," he said. "So, in order to change this technological situation, we have to change the Soviet economic," Ogarkov continued, "and in order to change the Soviet economy, we have to revolutionize the political system, and that Soviet leaders are unwilling to do." So he concluded: "Don't tell me your worries about Soviet military superiority."

I will add on my own that if this is accurate, Ogarkov would have been drastically overstating the situation with commercial computers. In 1981 the state-of-the art home computers in the USA were Apple II's and Atari 800's. These were command-line based machines that really smart kids could use, but not toddlers. They sold for the modern equivalent of about $5,000. So by 1981 there would have been some but certianly not a lot of recruits joining the military who had experience using one. However, when the Mac came out in 1984, yes toddlers could use it^*.

So you could argue the part about 3-year-olds was prescient exaggeration on Ogarkov's part, or an anachronism likely inserted by Gelb.

^{* - I can say this first hand. I had an Atari 800, and my parents bought one of the first Macs in 1984. My 4-year-old baby sister loved MacPaint, but her involvement with my previous computers consisted mostly of sneaking into my room while I was sleeping and gleefully unspooling my cassette tapes.}