There are the following possibilities:

1) The alcohol content of the ancients was not high.

2) Ancient vessels were very small.

There is another possibility, Qian, which means imaginary number and exaggeration here.

If there is a fact other than the above, it may be that this person often drinks at ordinary times, which leads to his body getting used to this situation, so as to achieve a thousand cups without getting drunk.

Hehe, my personal opinion, I hope it will help you!