These books are fun, but should be taken with some skepticism.
This particular story with large mammals is a good example. The assumed causality does not hold closer scrutiny. Climate was also changing into something that works better for humans, and into worse for large mammals. There were many things at play. Humans may had or may not have had a role. However, it is very unlikely that humans had a defining role.
Good read nevertheless! Changed my mind how I view humans as mammals, and made me dig deeper into the topic.