For those wondering: yes you can live without a stomach. The stomach’s main role is to mush up your food, called mechanical digestion. It is similar to what you do chewing your food, but it does this more than your mouth. There is also the bile that helps break down the food even more called chemical digestion, but your intestines do that as well.
Essentially, if you eat foods that don’t need mechanical digestion, you can live without a stomach. For a vampire that survives on blood, this could be possible and it is an interesting take on the vampire as a species story.