It means the drink is really strong. One sip will be enough to make the speaker so drunk that they won't be able to sit up. They'll fall under the table. "I'll drink you under the table" means I can drink more than you - you will fall under the table before I will.

I think I understand your question. It's an odd construction. 'YOU' is not the literal object, i.e. one does not drink YOU. It's an odd way of saying, "I will defeat you in a drinking contest." or "We will both drink, but you will end up under the table and I will not." Another common example of this construction: Eating us out of house and home. Ex? "Our son is home from university and he is eating us out of house and home." i.e. he's not really eating us . . . he is eating so much we won't be able to afford our house, metaphorically.

Not sure that I understand your question. If someone drinks too much, they will liekly fall down and then be possibly under the table. As you suggest, to drink somemone under the table is to out-drink them, to be able to drink as much as them and suffer a lesser effect, for example to not be so drunk as to be under the table, when they are. It's used rather figuratively to mean a lesser amount of drinking. . So in this sense in yellow, it means that one small drink and the writer would be drunk.