The question addresses elements under the two categories of absurdism and modernism in Beckett's play Endgame. As for the absurdist style and philosophy, the way the play problematizes the meaning of human existence and critiques rational thought are clear instances of this vision. But Beckett is not portraying a meaningless world here. He is portraying a dark and banal world after the two World Wars, where destruction is writ large over everything and there is an apparent pointlessness to hide the infinite problematization of meaning in a cryptically complex world of non-communication, confinement, banality, immobility and death. The tragi-comic vein suits the style to perfection too.
The Modernist elements abound in the play. Thematically speaking, the ideas of non-communication, alienation, psychic crisis, master-slave relation and so on all have such a bent. The play evokes the mythical structure of Noah's ark and the guiding pattern and metaphor of the chess remind us of the classic Eliotesque trope as in Waste Land. The formless form and the apparent plotlessness--all these are structural innovations that go well with the avant-garde and formalist bents in Modernism.