The Age Discrimination Act deals with the rights of the citizens of the US. The purchase and drinking of alcohol is a privelige, not a right, therefore the act does not apply to the consumption of alcohol. Below is an exerpt from another forum that answers the question much better than I can.
Basically states are free to restrict your right to liberty by law (via the state's broad "police power") unless the law infringes upon your "fundamental rights" (e.g., right to vote, etc.) Drinking is not a fundamental right. A law restricting something less that a fundamental right (e.g., drinking) need only be "rationally related to a legitimate government interest" to be constitutional. Here, the legitimate government interest is to protect youth from the so-called evils of alcohol. The age restriction is rationally related to that end. Therefore, the law limiting the age of drinkers does not violate the "due process clause" and is constitutional.
What about discrimination under the "equal protection clause"? Well, unless the law discriminates against a "suspect class" of people, the above analysis is the same. A "suspect class" of people is basically those people who have been getting a raw deal for years and years (e.g., minority races, religions, and people from certain nations, etc.) Discrimination on the basis of age does not affect a suspect class (minors). Since the law barring minors from drinking doesn't affect a suspect class, and it is rationally related to a legitimate government interest, that law doesn't violate the equal protection clause either. The analysis would be totally different if the law prohibited Argentinean-Americans or Muslims from drinking, or what-have-you.