Oh no, again this PageRank myth.
Google won, because it was fastest and had good links.
Fastest was more important than better links. How did they get
faster than their competitors? They bought cheap servers all over to beat the transportation times to the clients. Also their page was smaller, not overloaded, so the results could be presented faster.
Their bot was also more aggressive. A more aggressive bot contributes more to the link quality than the algorithm, because you get deeper and new stuff more timely. People are searching for new stuff.
That's how Google won. Not because of PageRank alone. PageRank was a contributing factor. But renting out cheap servers in every datacenter out there and keeping the page small and fast and dealing with the consequences of cheap servers (HD fails, fallbacks, ...) was more important.