Part I is mostly an extrapolation into the future, based on observed mutation rates in genes that regulate brain development, as well as a tiny lit. review on the processes that cause intellectual disabilities. One key thing to note is that these mutations involve actual intellectual and emotional disabilities, such as autism and down syndrome, not drops in IQ points. That people with these disabilities have a higher chance of survival in the modern age is kinda a no-brainer.
Part II is the controvertial one, where he claims that our ancestors must have had much more intellectual capacity. Most of his arguments there are entirely speculative and based on thought-excersises or "what-ifs". Not really a research article by any measure. I'd be surprised if it gets published as anything but an opinion piece. One of his key points here is that post-agriculture, selective pressures must have favored populations with high resistance to diseases rather than intellectual abilities, compared to hunter-gatherer societies where the later must have provided an advantage in fitness.
How true that is and how much impact it has is probably questionable. It's certainly a convenient oversimplification, and he doesn't provide any actual data to back up his point. Crabtree actually admits he is neither an anthropologist nor a population geneticist, so his claims should be taken with a heavy grain of salt.