This study looks at the effects more so of replacing red meat with plant-based foods, not so much the effects of replacing it with chicken which is what the per capita consumption changes so more there

There are of course a number of other factors indeed that influence diabetes, yes

Found the answer on npr:

It's difficult to unravel whether the meat itself, or some constituent of the meat, may explain the increased risk of diabetes. Another possible explanation is, people who consume a lot of red meat may have other things in common that could drive up their risk. For instance, excess body weight is a key risk factor for developing type 2 diabetes.

It turned out, the participants in the study who consumed high amounts of red meat also had higher BMIs. They consumed more calories and were less physically active compared to those who consumed the least red meat. Researchers used statistical methods to adjust for confounding variables. "We found that about half of the excess risk with red meat consumption was explained by excess body weight," Willett says, "but there was still an increased risk [of developing diabetes] even after taking into account body weight," he says.

source

So basically 50% of the risk was lack of activity/obesity, with the other half variable risks from things like (possibly even primarily) red meat.

They also account for weight in the study, the association is still there after that's accounted for

See this response earlier in the thread from another commentor https://midwest.social/comment/3882967