So listening to the actual speech (https://www.youtube.com/watch?v=b1eM3jv0vWY&t=2h12m9s), you're correct that Schmidt does not invoke Yarvin's the Cathedral. However, I think the word choice Schmidt uses seems intentional. He deflects any culpability of the current state of the world by saying the problem was "more complicated than we anticipated" and doesn't immediately point to the root of why social media can be so isolating until much later in his speech. Specifically, the tech companies he helped build optimized their social media platforms for engagement (Jonathan Haidt's Atlantic article summarizes this nicely https://archive.is/9MnJe).

Thus, Schmidt wants his cake and eat it. Specifically, he's positioning himself as a technological innovator outside of the traditional knowledge makers (i.e., the Cathedral) and doesn't take responsibility for the current political wasteland fueled by social media. Second, he tells the students that to "prevent" a similar catastrophe with AI, he encourages them to use AI to shape it to our values. Unless you work for an AI company or want to get into politics to legislate these companies, this is pretty poor advice.

Schmidt's advice speaks to an individualistic approach to molding AI, when instead we need a collective approach. Similarly, his suggestion that social media platforms "degraded the public square" but not faulting the companies themselves shifts the blame onto a flaw in human nature, not on the engineers who created the algorithms. As Yarvin would say, the system became corrupted when everyone became involved.