Compute absolutely matters. With tree search, there's a tradeoff between scoring cost and positions evaluated. AlphaZero can evaluate fewer positions because it uses a huge amount of compute to accurately score each position.

It's not just training. Training used 5,000 TPUs.

Can't those teraflops be applied to evaluating more positions instead of deciding which positions to evaluate?

It seems that the metric should be compute time, not positions evaluated.

Presumably they both had equal clock time - that is a standard chess rule so it would be surprising to see it different.

Wall clock != cpu clock

I can do more in the same wall time with a faster cpu(s); I can afford inefficiencies that the opponent cannot, and accomplish just as much.