I pulled up the full paper. As you speculated, people who skip meals are quite different from people who don't, in ways that
might be relevant to overall health outcomes:
> As shown in Table 1, compared with participants with three meals per day, participants eating fewer than three meals per day were more likely to be younger, men, non-Hispanic Black, with less education and lower family income, current smokers, heavy alcohol drinkers, higher physical activity levels, lower total energy intake and lower diet quality, food insecure, and higher frequency of snacks.
They control for these factors in the statistical analysis, to different extents in three different models:
> Model 1 adjusted for age, gender, and race and ethnicity. Model 2 additionally adjusted for education, income, smoking status, alcohol intake, physical activity levels, total energy intake, HEI-2010 score, household adult food insecurity status, and snacks frequency. Model 3 further adjusted for baseline diabetes, hypertension, hypercholesterolemia, CVD, cancer, and BMI status, because these variables may be mediators between meal frequency, intervals and timing, and mortality.
This is an issue. Controlling for the variables in the model helps somewhat, but it's inevitable that the populations are also different in other relevant ways that are not captured in the covariates (e.g. stress levels).
They're also reporting dozens of results (18 in Table 2, another 18 in Table 3, 12 in Table 4) but doing no correction for multiple testing. Given that many of the confidence intervals only barely exclude 1, this is an issue.
Finally, and most damning--the effects almost entirely disappear if they exclude people who had cancer or cardiovascular disease at the beginning of the study. This is hidden in the supplementary material of the paper, not discussed at all within the main body of the paper. Of the effects cited in the abstract the only one that survives excluding people who had cancer or cardiovascular disease at baseline is that people who skip breakfast appear to have higher risk of cardiovascular disease-related mortality.
Given that the study is labelled "prospective" and one of the outcomes studied is death from cardiovascular disease, IMO it is dishonest to not note that the claimed effects disappear if you exclude people who already had cardiovascular disease when the study started.