If magician youkai are anything to go by, youkai in general don't actually need to eat to survive.
A vampire's need to drink blood could just be one of their many, many weaknesses. Most youkai don't fear sunlight, running water, garlic, AND fried beans. Vampires are uniquely unfortunate like that, and survive only because they're otherwise as powerful as oni.
Case in point, if Rumia actually needed to eat to live, she'd already be dead. Her "hunting behavior" is simply too stupid, what with flying blind into trees because she won't accept anything less than total darkness or else just sleep through the day.
There's just no way she can run into that many humans dumb enough or unlucky enough to fall into her clutches. Not in Gensokyo, and neither Yukari or Ran will waste the time to feed her with kidnapped humans.
Also, the number of humans it would take to feed the Tengu and Kappa as well as the Oni of old would have depopulated Japan in the ancient days.