I can see how this statement applies. Although Beckett himself famously stated of his work, "no symbols where none intended," it is almost impossible not to see symbolism in what he has written. Like "Endgame" the play revolves around two main characters who ate somehow isolated, stuck in a repetitive pattern, unable to make a move to do anything differently. Vladimir and Estragon are waiting, ostensibly for "Godot" - but who they are waiting for is not as important as the fact that they are waiting foe someone (or something) that they have never seen before but that they anticipate will arrive. They will not act until that moment occurs, so they are doomed to repeat the same process over and over again.
Where I see a clear parallel here to the modern world is that we, as a society, often repeat the same actions without giving any though to what they mean. We do what we are "supposed" to do according to our society, but as was a major theme of the modernist period in literature, we do not know for certain why we do those things. The world has lost its sense of meaning just as it has lost its humanity. We are obsessed with the idea of "progress" yet we do not know what that really means. At the same time, we suffer from an inability to act. We wait =until we are told what to do, we never step outside of the accepted and expected norms. We stagnate and we lack an internal driving force to break free from that stagnation - in this sense, the world is empty, disillusioned, and devoid of purpose.
I think that it is important to keep in mind that the play itself is difficult to find a transcendent meaning. Part of this might be that Beckett himself was too elusive a writer or thinker to capitulate to such an idea. He would want to keep a sense of the vague present and this is probably where the question would find itself. I sense that the characters in the play do grasp, to a certain extent, the emptiness of their lives and interactions, and their purpose in waiting for Godot. I don't think they operate in a realm that is outside of this. I sense that the characters understand their sense of emptiness and meaningless, but like the paralysis that overcomes them despite their assertions to the contrary, there is little that can be done about it. I think that this might be where the play operates; articulating and understanding a condition that one is unable or incapable of doing anything about.
While the first part of the statement is beyond doubt, I am not so sure about the exactitude of the second part. Among other things, Waiting for Godot is surely about the emptiness of the modern world but whether this world knows itself to be empty or not is a tricky question. In general with a maximization of the culture of jouissance or enjoyment in today's late-capitalist world of alluring specualrity and simulations, the notion of emptiness does seem to be unacknowledged, but I think, Beckett's art is replete with an ethic of admitting the truth of the mess, what he once called shaping the chaos that surrounds us in a new aesthetic form.
Godot may not be a pinnacle of Beckett's new form but is surely a move towards it. Beckett's art shocks us out of our capitalist and bourgeois complacency in its ability to shock. There is a real of thought at the level of unconscious that always admits the hollowness. We just have to listen to its voice. I think Didi and Gogo do listen to it. Consider Vladimir's first speech 'Nothing to be done' or his 'Was I sleeping' speech or Pozzo's abrupt disturbances and above all the admission in Lucky's great speech.