Do you have any specific criticisms in mind? That abstract implies that the paper doesn't actually argue with anything in GGS itself. Rather, "environmental determinism" sounds like it's a dirty word in their niche of academia, and they need to yell at GGS because it might be contaminated.

One way to phrase the distinction is that no one really expects huge empires in Antarctica, so everyone admits there's some role to the environment. GGS talks about more complicated effects that the environment has, without saying anything about the outcome being deterministic. It argues that the odds were somewhat higher of Europe invading North America than vice-versa, and doesn't even try to quantify by how much.

With the disclaimer that I've watched the documentary and haven't read the book, the reasoning seemed faulty and unsound to me. It was definitely too deterministic and did not really go into non-environmental factors. For example, it boiled down the state of development of Papua New Guinea civilizations to the primary source of starch being palm trees vs grains, or something to that effect. It feels like picking one contributing factor and focusing on it at the expense of everything else.

I didn't see the documentary, but the book does build a single case, but it's mostly saying "please consider the many, many complex effects of the environment" rather than "don't consider other things."