The winner if there is one will be clear. Making a machine that's as good or better than human at most tasks is the turning point but doesn't demonstrate the win. Applying it for self-improvement making superintelligence which is when the winner will be racing with rockets vs bicycles. I don't know how this will play out--will the second one to achieve it always be behind? It probably depends on the difference in timing and other factors.
The winner will be the one that announces "we have AGI" based on their own definition, and the rest of the world actually agrees with them.
The upside of being right is massive, but the downside of prematurely announcing AGI only for the rest of the world to disagree with your definition is probably tremendously large.
For example, a "space race" might be "won" by the first participant to reach space, or to reach the moon
Is it possible to have a "race" without a time limit or a finish line or some way to determine the "winner"