One of the crucial things to understand when dealing with Chess is that it was conceived of as a very timely musical, dealing with east/west tensions and the odd phenomenon of chess celebrity in the West. However, as the 1980s went on, the relations between the United States and the Soviet Union changed dramatically as the Soviet system went through its final crisis. The US switched from "evil empire" rhetoric to a much more open stance, as the USSR under Gorbachev embraced "Perestroika" (reform) and "Glasnost" (openness).
At first, Chess did not pretend to notice this; the London production was set in 1986 and assumed that things would be in uneasy detente for the forseeable future. But signs of cold war thaw hit the 1988 Broadway production, and the first place that it showed was in the lyrics for "US versus USSR" (credited in the score as "Diplomats"). The ominous couplet "No one can deny that these are dangerous times / These are very difficult and dangerous times" gave way to an upbeat "No one can deny these are encouraging times / These are optimistic and encouraging times," which was to see its way through to 1990. Half of the Broadway show was set in Hungary, and the script refers to it being a diplomatic conference that gets the then-defector Anatoly into the country.
By the wave of regional and touring productions that began in 1990, the cold war was effectively over. So-called "communist" regimes in Eastern Europe were falling, and Gorbachev's changes had made a significant impact. The Berlin Wall was gone, which caused a small lyrical rewrite in "Embassy Lament" for the 1990 Sydney, Australia production. The American Tour in the same year had references to Gorbachev and the first President Bush, and talked about "cold war revived as chess tournament." These are the two productions that are affected the most by political reform. (The American Tour infamously was followed by its script doctor, Robert Coe, who was reworking material as he went to fit with current events.)
The most immediate problem of glasnost and perestroika is that they made Anatoly's defection from the Soviet Union almost paradoxical. As the show moved away from the early to mid 1980s and the cold war, the reporters' questions for Anatoly before "Anthem" (a mainstay of all the major 1990 productions) become half-confused; the American Tour outright says that Anatoly has the freedom of travel he would have lacked in 1986 or even 1988. Without the onerous travel restrictions of a Soviet citizen, the defection is more of a personal than a political statement, and almost certainly loses the intended punch (which was to parallel Anatoly to Viktor Korchnoi, a Soviet grandmaster who left Russia because he was blocked from rising to the top of the Russian chess circuit).
Even handling the defection in stride, glasnost blurs the role of the KGB significantly. It becomes more difficult for Molokov to be the villain of the piece, and by 1990 his part (especially in the second act) is more one of saving face, as was dealt with quite explicitly in the extensive Sydney rewrite of "The Soviet Machine." This tended to fit well with the fundamentally sound dramaturgical decision to focus the show around a single chess match that was used in Broadway, Sydney and the American Tour; Molokov, rather than trying to stage a match a la Karpov/Korchnoi 1978, is primarily concerned with getting Anatoly home. Changing this, in turn, becomes something of a problem for "Endgame," where the original point of the match was that Anatoly had to lose to Viigand. Stripped of this, Anatoly can lose the match in Broadway and the American Tour, but the scene loses some of its pure climactic impact. (I will discuss the issue of "Endgame" further in a later post.)
The material in the Sydney and American Tour productions inevitably runs into the glasnost and perestroika issues, and from the vantage point of 2006, it is almost impossible to justify a time setting other than 1986 or a few years before it. For both, this would require some cutting; the operation in Sydney is more delicate, because pushing it back to 1986 makes Florence too young to have been a child of the Prague Spring, and these references would have to be replaced with the traditional Hungarian story line. In the American Tour, it can be well argued even by those friendly to the Coe script that the "topical" jokes have aged poorly, and the text (which was thrown together in a few weeks) is already in need of a significant revision. Personally, I am convinced that it would be a worthwhile venture to turn back the clock should one decide to move forward with either script.