Existential elements in Eugene O'Neill's Long Day's Journey into Night include the meaninglessness of the world, the focus on individuals, the subjective, and the concentration on emotions. Let's look at each of these in turn.
Existentialists believe that the world itself holds no meaning but that humans must create meaning for themselves through their choices. In the play, the world holds no meaning for the characters, yet they fail to create meaning for themselves. Mary gives into the apparent meaninglessness and becomes addicted to morphine. James cannot pull himself out of his disappointment as a once popular but now failed actor. Jamie and Edmund seem more intent upon getting drunk than making anything of their lives.
Notice, too, how the play focuses on these four individuals and their choices. This is another nods toward Existentialism as is the subjective stance of the characters. They will not see reality for what it is. They view life from their own perspectives, caught up in their own misery, slaves to their own emotions.
Emotion, of course, is at the center of the play, and this also reflects existentialism, which puts a high value on emotion over intellect and reason. The characters are not at all intellectual. They are driven by emotion, and this is nowhere more evident than when Mary comes down the stairs in her wedding dress at the end of the play. She has completely turned herself over to her misery.