Yes, he assessed the situation back then correctly. That was not hard to do. He said it himself in the interview "do the math" to indicate how this was a no brainer.
What he didn't foresee was that the world would change in a way that makes a +4$ billion "content club" business viable.
The journalists don't put their cards on the table. Were they pressing him so much because they thought a +4$ billion "content club" was possible? This is not clear from the video.
If they thought so, was this out of naiveté or foresight? Of course I can't tell, but back then Wired was much better than today, to say the least.
Considering Gates was referring to "content clubs" as akin to "record clubs" and the Wired interviewers were instead bringing up the cable companies and Disney, I would say the Wired team had a good read on the future. Although other commenters here bring up a good point that Gates may have been downplaying the potential market for content creation/delivery on the internet. Also his dismissal of internet advertising is likely the gap Google needed.
And to me it seems he was spot on. The whole world and industry had to change before anyone could achieve that.
Your own links tell how much the growth has been in recent years. The interview was in 1996.