If people see a universal element to The Gin Game, it's because the conflicts are so basic to our nature and are distilled to their most basic levels. There's the man, the woman, our will against each other and our will against God. Those are very clearly defined conflicts that are the same everywhere.
I would not call this a very American play, although I'd be very proud and happy if it were called a American play. I don't think The Gin Game plays in other countries as an American play. Germany comes second only to the United States in the number of productions that have been done. There have been an enormous number of productions over the 25 years that the play's been in the world repertory.
In England, there have been two West End productions. In Italy, they've had major productions and major tours. The audience response to the work is the same the world over. Only in Russia was there a little difference. They tinkered with the end of the play, because they said they didn't like unresolved endings.