Read the whole paragraph.
>Oddly, either the book or the Kleiner-Lott paper might >count as the
>"refereed" work the Clay Institute demands. If so, we >would have the
>weird situation in which authors of the work that >satisfies the prize
>requirement aren't the people who figured out the proof. >But their
>efforts could win Dr. Perelman $1 million.

The book and the Kleiner-Lott paper did not claim the
credit of the proof of the Poincare conjecture.
What they claimed is that Perelman's proof is true.
Therefore, "their efforts could win Dr. Perelman $1 million."

Zhu-Cao's paper is different. It claims to
give a "complete proof" of the Poincare conjecture.
If Zhu-Cao的文章满足条件, then $1 million goes to them.