In the Spuniks game I run annually (two teams of five, semi-annual turns), we've made it to 1973. In our universe, the Americans landed in July 1969 (using EOR, no less!) while the Soviets managed to roll incredibly well and land a cosmonaut in October '69.
The Russians, by the way, knew that their success had been a fluke, and having won the propaganda victory, shelved their lunar project and have been focused on space stations. The Americans were flush with funds for a few months, but then Congress cracked down. The Americans will have to make some hard choices re: priorities. I'm hoping there's enough momentum to get the Saturn II built, because that will make the exploitation of space a bit cheaper.
I'd love to see both sides decide to team up on lunar exploration, sort of an ASTP writ large.
You are going to have to show me this game. I am a fan of BARIS (Race Into Space) but I have often found it lacking in that you really can only land on the moon and then game over. I believe I had once seen a summary of the game, but nothing beyond that.