"A beer? You drink alcohol?"
Translation:Une bière ? Tu bois de l'alcool ?
Correct. "boire de l'alcool" when the amount is not defined and "boire un verre". There's a good summary on Definite/Indefinite articles here: http://www.languageguide.org/french/grammar/articles/
This example is partitive ("some") for the alcohol bit, for some reason other comments seem to be saying this is definitive. The confusion may be that this is not "de la" or "du" however when the noun starts with a vowel, whether masculine or feminine, "de l'" is used (de l'alcool) for the partitive.