To clarify, it's specifically squamous-cell carcinoma, not all esophaheal cancers. SCC is, however, the most common form of head/neck cancer by a mile.

As the study notes, though:

As discussed above, the higher risks we observed for squamous cell carcinoma of the oesophagus in vegetarians, and for colorectal cancer in vegans ["although the number of cases among vegans was small"], might be due to a higher prevalence of inadequate intakes of some nutrients in these groups within the populations studied.

If so, that's a highly preventable problem. Vegan/vegetarian diets have higher risks of certain nutritional deficiencies (and lower of others), but it's not especially hard to have a balanced diet.

That is: if you're doing it for health, the "fix" should already be baked-in.

Edit: Forgot to mention for anyone looking for resources about vegetarian/plant-based dieting for health, "whole foods plant-based" (WFPBD) is what you'll want to be looking into. That's where the major health benefits are.

Edit 2: Reading the methodology more thoroughly now, it seems like a plant-based diet was underrepresented in the data and that "no difference in cancer risk in vegans except elevated colorectal cancer" is suspect (which the authors disclaim for colorectal). a) Within the study itself, you'd think the doubled SCC rate wouldn't just stop at vegetarians somehow (a plant-based diet is less acidic than an animal-based one, but still??), and b) it directly contradicts several meta-analyses finding an overall lowered risk of cancer in vegetarians (as this study seems to) and then another marked lowering from that in vegans. Linked above, for example, from 2018:

This comprehensive meta-analysis reports a significant protective effect of a vegetarian diet versus the incidence and/or mortality from ischemic heart disease (-25%) and incidence from total cancer (-8%). Vegan diet conferred a significant reduced risk (-15%) of incidence from total cancer.