This play is a stage drama focusing on the conflicts plaguing one family, the Tyrones. Even if no one dies at the end, the play is a tragedy: it documents the downfall of the House of Tyrone. In most tragedies the hero has a fatal flaw or makes some error in judgment. Each of the Tyrones has at least one tragic flaw with which they're slowly destroying themselves. James is miserly and an alcoholic, Jamie is a gambler and an alcoholic, Edmund has consumption and is an alcoholic, and Mary is addicted to morphine.
Often times, Greek tragic heroes are victims of fate. Take Oedipus for example. He was doomed from birth to kill his father and sleep with his mother. Unknowingly, he does just that. A comparison can be made to the Greek notion of fate and the idea of the past controlling the future. We learn over the course of Long Day's Journey into Night how events in each character's past made them into who they are. Though the Tyrones aren't powerless in the hands of the gods (like many Greek tragic heroes), they are certainly prisoners, in a sense, to events that are no longer under their control.