The Belarus transit visa issue was a critical issue for many fans, that plan to visit Minsk and other cities. As well as taking a flight or a train, including Free Trains between Kaliningrad and Moscow.
Today a new agreement between Russia and Belarus was signed: a temporary agreement on mutual visa recognition for the upcoming large sports events. It means, that World Cup FanID can be used to cross Belarus border.
Still to find an official text of the agreement, but I believe that the Belarus Transit Puzzle is finally solved.