Transferring heat with a smaller fan requires less power to run the fan. For a given amount of electricity, the Sandia Cooler can extract more heat from the processor, so it requires less electricity to keep the processor cool.
Not just CPU fans. FTFA, and the latter part of which was included in the GP's quote:
"an ideal replacement for just about every fan-and-heatsink installation in the world... For the most part, these savings would come from air conditioning and refrigeration systems..."
I know, I read that. The impression I got from the article was that these new heatsinks were going to be used on the CPUs and that somehow that would generate less heat. e.g, if Intel makes a lower power chip, a lot of savings will come from AC, even though Intel isn't making AC systems. It was not obvious to me (and I still have my doubts) that "every fan-and-heatsink" was referring to AC systems as well as CPU heatsinks.