This response will be a challenging response to understand, primarily because the topic is nearly impossible to quantify. In my mind, talking about Beckett's work is similar to putting your hands in a pot of honey; you are able to get a hold of it, but once you think you have got it, watch how it slips through your grasp. After reading the play, I presume you know what's going on with it. I don't sense that you are asking what the play is about; you already got that. The reason you came here is, I suppose, to ask yourself why there is meaning in what it is you read. I think this would be the point where the hand is placed in the vat of honey.
Let's assume the critic is right- that the play is an example where "nothing happens twice." We can then make the assumption that the character display the best and worst aspect of humanity, discuss elements that define existence and represent triviality, study themselves and one another, and interact with success and failure with each-other and others. They do all of this, and yet nothing happens... twice. I cannot even pretend to be an authority on this play because A) I think it's impossible to be an expert on something that is not meant for us to dissect and represent a totality of understanding and B) I don't think Beckett really felt that anyone can be an expert on it, and this would include himself. All I can do is examine what happens, assemble something, and determine an answer that is symbiotic, benefiting the pristine beauty of the play and enhancing my understanding of it.
The element that I am left with after the conclusion of this play is that precisely nothing happens... twice. These characters live, love, disparage, compliment, converge, and diverge and nothing happens twice. Their hopes are never quite realized, their words never lead to action, and what is indicated is never quite actualized. Godot never arrives. Despite all the uses, fancy and not fancy, of language, nothing happens... twice.
And I think that this is the precise beauty of it. The theme of paralysis is an overwhelming one in the play. It seems to me that action is prevented because of the belief that Monsieur Godot is going to arrive. The character praise him, hate him, deride him, mock him, and do this to one another. Yet, he does not arrive and they still wait... twice. The element of this play is that we all have to endure what the characters do. We all undergo moments when we are Lucky or Estragon. We are even sometimes the little boy who says that "Monsieur Godot will not arrive, but will be here tomorrow." The paralysis of these character is seen in us. Perhaps, the symbiotic way to examine this is that while the traits of paralysis and inaction are there, both on stage and within us, perhaps, unlike what is happening on stage... twice, there is something we can do about it. If we listen to the cries of others' suffering and seek to transform what is into what can be and overcome our own sense of paralysis, maybe something will happen... once. Perhaps, we no longer have to wait for Monsieur Godot to arrive.
The closing point. In a recent Bollywood film, Jaane Tu Ya Jaane Na, the closing scene takes place at an airport where there is a sign for the passenger, "Godot." The person holding it is quite old, presuming that he has been waiting for some time. If Bollywood can grasp the futility in waiting, I suppose I can, as well.