Why? A contest really is just a bunch of people… running together to see who gets tot the finish line first.
From that same Latin root, we get the English… concur. Why? It could also mean in Latin an “assembly”: a bunch of people might be running together, but might also be just talking together in an assembly, to which they come to a conclusion together, to which, they concur.
We can see the c-n-c-r root in both words clearly.