I also don't like that argument (even when presented correctly) because it ignores software and assumes you can brute-force everything.

Shane Legg prepared this graph.

It was enough to convince him that there was some super-exponential synergy:

I dont disagree with the idea of an A.I. Intelligence explosion, but I do think their argument is the wrong one. It is a fairly common idea though, especially from semi-laypeople, so I'm not surprised to have seen it in their video.

Everything else in the video seemed roughly accurate, though.

I'm pretty sure that was Kurzweil's claim originally. Can't remember if they attribute it to him in the video or make it themselves, though.

However, they make the claim that the doubling period for Moore's Law is shrinking, which I think is false.

It's demonstrably true, widely documented, and well understood. Don't be spreading misinformation.