He seems to suggest that "humans = chimps + X", therefore what makes intelligence must be a subset of "X", therefore rather small.

Which in my opinion is wrong. Imagine that to make intelligence, you need A and B and C and D. Chimps have A and B and C, but they don't have D. Humans have A and B and C and D, which is why humans are more intelligent than chimps. However, having D alone, without A and B and C, would not be sufficient for intelligence.

The fact that the DNA distance between humans and chimps is small only proves that if we tried to make chimps smarter by genetical engineering, we wouldn't have to change most of their genes. But that is irrelevant for making a machine. We don't have fully chimp-level machines yet.