Well a couple of ideas:

The death in the play may signify that Emad and his wife have "died" a little inside.

The turning off of the lights in the apartment means "the play is over".

And the final scene where they are both in make up and masks sitting in resignation may mean that they have decided to put up an act and never speak of that again at the cost of loosing the life in their relationship. They choose to act like it is all over and it doesn't matter.

Actually I misunderstood your question. I was commenting on the significance in the movie that I understood. I haven't read the play and I only base my ideas on the parts of the play that were presented in the movie.

Here you can find some info about your question in specific:

The Guardian review

I've not seen or read the play for many, many years. But I really don't get much parallel between Emad in the film and Willy in the play. Its almost incidental to me. I don't think Emad was remotely disillusioned and impotent with the events that unfolded. Uncertain and conflicted yes, but I don't see what that has to do with the themes of the play. The focus of the film was almost entirely on the marital relationship, which is only a minor aspect of the play.