Lets take a look at the Pythagorean W-L records for some of the contending teams this year.
New York Yankees: 95-67
Boston Red Sox: 93-69
Los Angels Angels of Anaheim: 92-70
Minnesota Twins: 86-77
Philadelphia Phillies: 92-70
St. Louis Cardinals: 91-71
Los Angeles Dodgers: 99-63
Colorado Rockies: 90-72
No one is denying that the Yankees have a huge advantage off the field. That's undeniable. But how much is it really translating to play on the field? If you just take a look at this year (a year in which the Yankees won the championship, because past years would even further prove my point), were the Yankees significantly better than the other seven teams that made the playoffs?
According to PYTH, the answer to that question is no. In fact, they weren't even the best team this year. The difference between the Yankees and the Red Sox is two games. In terms of who was better, that difference is negligible. If the Red Sox get a break here, or a break there, they easily could have had a better year than the Yankees.
So I think it's important to note that while the Yankees spend so much more money than anyone else (which, again, no one is denying), they don't have nearly that same advantage on the field, where it actually counts.
EDIT: Also, according to the article of the author, the Yankees began separating themselves from the rest of the pack (in terms of payroll), starting in 2002. Now when you say "win more" I'm going to assume you're talking about winning the World Series, because, in the end, that is what constitutes a successful season (I guess some clubs don't see it this way, but a decent amount do).
2002 World Series winner: Anaheim Angels
2003 World Series winner: Florida Marlins
2004 World Series winner: Boston Red Sox
2005 World Series winner: Chicago White Sox
2006 World Series winner: St. Louis Cardinals
2007 World Series winner: Boston Red Sox
2008 World Series winner: Philadelphia Phillies
2009 World Series winner: New York Yankees
Eight champions have been crowned over that time span. The Yankees have won 1/8 of the titles. The same goes for the Angels, the Marlins, the White Sox, the Cardinals, and the Phillies. The Red Sox have won 1/4 of the titles. I know all this stuff is obvious, but it helps to make a point.
According to you, the Yankees will win more, and they have won more. However, the facts do not back that up. The Yankees might go on, over a much larger sample size, to win a higher percentage of championships than anyone else. But, and most importantly, that is conjecture. You're speaking of these things as if they are based in fact. Part of what you said is incorrect, and part of what you said is conjecture. None of it is fact.