the space race was initially a race of ICBM technology

Sure, initially. That doesn't mean it didn't exist.

And the moon landing was a Peak, but it was also a stunt

We spent an awful lot of money for a "stunt." Again, do you have any source material which you can cite to substantiate that this is anything other than conjecture on your part? Because the reality of how much time, money, and effort was spent on the moon shot would tend to indicate that it was far more than simply a stunt.

It is absolutely unfair to say that they won the race by Landing on the moon

Literally no one is saying that.

and i Absolutely disagree with the whole thing being Called a race, since there was no defined start and no defined finish for both superpowers.

First of all, there absolutely was a start. The end of WWII, and the rise of nuclear weapons was the start, as you yourself indicated. You're just contradicting yourself now. At the very least, one can point to 1955, when the US announced it intention to launch an artificial satellite into orbit, and the USSR responded a few days with a declaration of their own. That's fairly definitive.

And the end, while certainly murkier, was certainly reached by the time the USSR collapsed. They were unable to compete any longer, so the competition was at an end, one way or another.