No non-American has ever walked on the moon.There have been astronauts from several countries, including Russia, Sweden, Britain, Switzerland,......
Soviet Russia put the first DOG into space -- Laika, who died in orbit
Russia put the first MAN into space -- Yuri Gagarin
But after that, the poor Russian economy, run by a communistc, socialistic dictatorship, didn't have money to make any more moon attempts after the Soyuz paunches. A very similar situation is happening in the United States right now.
So the United States "won" the race by being the first country -- and ONLY country -- to ever put a man on the moon. No non-American has ever walked on the moon.
There have been astronauts from several countries, including Russia, Sweden, Britain, Switzerland, South Korea, Japan, and others, but these have gone ONLY to the International Space Station, and NEVER to the moon.
Rumor has it that China is now working on a possible Man on the Moon program.
"All countries" were not competing, just the US and the Soviets. By the time people really stopped caring in the early 1970's, the Soviets really didn't have the resources to send people to the moon. The only reason the Soviets were "winning" in the earlier space race is because they were willing to put headlines before safety (like by forcing 3 people into a 2-person capsule). Most of the early unmanned Soviet trips to the moon failed. The USSR did do a robotic sample return mission to the moon in 1970, but by then there was no real strategic reason to send humans.
I think that the 'race to the moon' you're talking about is the unmanned race. In this race the US landed on the moon first, then everybody else involved in 'the race' landed in the moon later. Then when the US went looking to put a man on the moon everyone thought it was impossible and left the seamingly impossible feat to the peaple who had beaten them in the first 'race'.
Hope this helps.
they have hamburgers.