The first thing to notice about this question is that it really isn't about quantifying objects. The second thing is that it's not about the verbs eat and drink. Instead, judging from the example sentences, it's about the generic use of verbs.
Notice that every example sentence is in the present tense, and involves an active verb. That makes it generic; i.e, it's not describing the present time (that's what the present progressive is for), and it's not describing the past or the future, except by implication -- instead, it's describing generic, habitual behavior. Generic use of an active predicate essentially converts it into a stative predicate referring to repeated (if possible, identical) events.
That changes all sorts of things, like the fact that if I say I eat meat, for instance, I may eat 10 grams at one time and 100 grams at a different time, without affecting the truth of the statement I eat meat. I may eat half a cheeseburger, or three at one meal, ditto.
And this is true not just of eating and drinking (though it's true we do talk generically a lot about eating and drinking; the sense of these verbs used generically is to comment on personal or social tolerance of various food and drink; if you say I eat yogurt you're indicating at least that you tolerate it. You're not really summing up all your yogurt for quantification.
This lack of quantificational rigor is true of practically any transitive active verb used generically:
- She knits sweaters for cats. (how many sweaters, how many cats? Who knows? Who cares?)
- He reads science fiction. (A singular mass noun object)
- He reads a lot of science fiction. (quantified = He reads science fiction a lot)
- He reads science fiction novels. (a plural count noun object; plural because repeated)
I could go on at some length. Fortunately, however, I already did, and for more than anyone sane could possibly want to know about English generics, see Studies in English Generics.