Yes, this new study has limitations. The authors do note that and aren't pretending otherwise. This is coming in the context of other studies with similar conclusions which the original article talks about. This new study is a singular imperfect data point, but is combined with other data points that point in the same direction.
What it is primarily helpful for is in that it has a large N value of 79,468 participants and the population they are looking at doesn't partake in as many carcinogens that make it harder to tell cancer rates apart (which is both a strength and also a study limitation too)
From the study
This study has several other strengths. 1) This is probably the single cancer cohort with the largest number of vegetarians, and especially vegans, who have rarely been studied effectively for cancer incidence.
This allows consistent definitions and methods to be applied across all variables; 2) in many studies of vegetarians, vegetarian diets may be relatively transient for some subjects, but less so in AHS-2; 3) the level of validation available for the main variables on which the assignment to vegetarian diets is based; 4) the relatively large Black subgroup in which vegetarian diets have rarely been studied. Race is always a co-variate in our statistical models; and 5) the absence (practically) of cigarette smoking, a common confounder for many cancers, and very little alcohol
There are also study limitations, the most prominent of which is still the relatively small numbers of less common cancers, particularly among the less common dietary patterns (vegans and pesco-vegetarians) that diminish statistical power; second, there is the relatively health-conscious low-meat-consuming reference group, the Adventist nonvegetarians, that also limits power; third, that we were able to measure dietary and other data only at study baseline and not during follow-up. Finally, there are the limitations of all observational studies, particularly the possibility of unmeasured confounding, which can be limited but never avoided