You're correct that many of the p-values are off. Even some of their Fisher Exact tests are off (e.g. I get p=0.47 for hypertension). I think they probably used Mann-Whitney U tests after a Shapiro-Wilk's p<0.05 for many of these, but I can't prove that without access to their data. It is odd overall.

I will point out they claim to test their primary hypothesis by ANCOVA accounting for baseline values, and randomization is not necessarily pointless even if you don't end up with well-balanced groups by specific endpoints. With that said you could probably get a response published on the basis of some of these discrepancies.