While the movie's title suggests drunken fighting, Fei-hung's fighting style is based on the "Drunken Fist" martial arts form, which uses the appearance of drunken movements to confuse and disorient opponents.
He does, however, drink a herbal tea that his father gives him before a fight, which is meant to help him relax and focus. This tea is what allows him to access the Drunken Fist style.