Beckett wrote his plays in French and then translated his own work into English; that might partially explain the eccentricity of his dialogue. In attempting to verbalize the Beckett-ian system, or rhetorical context of his work, the reader should start with existentialism. More specifically, I think Beckett is saying that the devices of civilization have proven to be meaningless, and this determines how estranged or interdependent people have become in response, acting out their anachronistic social roles to create a solid existence from nothingness.
The setting is a room. The quartet of characters, Hamm and Clov, and Hamm's parents, are each impaired or paralyzed and live further compartmentalized existences. Master and servant do everything they can to function within their biodome-like isolation. Their conversation is clipped, rendered into shorthand, things already said, repeated in a ritualistic loop. They're a bickering duo, as if they are former WWI soldiers, forgotten in their trench, or a Vaudeville comedy team, shunted to progressively lousier venues as time itself winds down. Beckett's intensive stage directions are actually reminiscent of twentieth-century comic mastermind Stan Laurel's charted-out slapstick routines. This is dark comedy, or—more accurately—Absurdism. What we come to understand about the characters' dire condition makes it counterintuitive that anyone's even alive to tell their tales.
There's despair, and there's some hope. Hamm sees light on the kitchen wall; then it shines no more. This moment could suggest the symbol of "writing on the wall," a classic omen of imminent doom. A starving child appears in one of the fables told that night. Later, he might be actually be physically hovering outside, beyond the stage. Notice of his presence offers a slim hope for the future. One hint that the author doesn't simply want his audience to be appalled at the squalor of humanity is the perverse resilience the characters display in their private wars of attrition. Not surprisingly, Endgame has to do with endings.