Why are people in the hospital? If they are in BECAUSE of covid then this would suggest the vaccines do nothing. But if they are in for other things (broken bone, surgery, etc) and tested positive for COVID while in there then it suggests that hospital populations are representative of the vaccination rate (i.e. it's equally likely both vax and unvax people can get COVID) but says nothing about comparative severity.
Given the "rigor" this guy applied to his analysis it says nothing about nothing.