The play is a drama because, well it's a play – a piece of literature that can only be fully appreciated when presented before a live audience. More specifically, we dub it a tragicomedy, because it blends elements of both tragedy and comedy. Throughout the play, serious subject matter is combined with dark humor to great effect. The style of tragicomedy is typical of absurdist plays. Samuel Beckett's Waiting for Godot is another famous example. It's no surprise that these two dramatic works are both tragicomedies as Beckett was one of Albee's main influences.
Shakespeare also wrote what scholars call tragicomedies. A Winter's Tale is one such example. In these plays the action progresses forward in tragic fashion, but instead ends happily. Absurdist tragicomedies, however, rarely end with what most people would call a happy ending. In Waiting for Godot, for example, the characters are trapped in a meaningless endless cycle. Are George and Martha trapped in the same sort of thing, or have they been liberated by their shedding of illusion?