As SC said, the dates are all screwed up on the extra scenes. But, Rudik, you're inferring a mistake that isn't a mistake:
The written intro to that deleted scene says "1917." The "Black Sox" scandal, in which Arnold Rothstein was alleged to have fixed the World Series, occurred in 1919. But Arnold Rothstein was one of the biggest underworld figures in New York way before the 1919 World Series. So, when Clemenza asked young Roth, "Who is the greatest man in the world to you?" and he replied, "Arnold Rothstein," the youngster didn't have to be referring to the 1919 Series scandal.
Later, when Michael calls on Roth in Miami in 1958, Roth says that he's been a big baseball fan "ever since Arnold Rothstein fixed the 1919 World Series." That's probably where your confusion originated.
Two other points:
First, Rothstein didn't fix the 1919 Series--Abe Attell, a crooked boxing figure, is usually mentioned as the fixer. But Rothstein knew about it and profited from the fix. The character "Meyer Wolfsheim," who appeared in the F. Scott Fitzgerald novel "The Great Gatsby," is based on Rothstein.
Second, in that deleted scene, "Roth" says his name is "Hyman Suchowsky." Then Clemenza says, "But we give him a better name" (which is how he became "Roth"). The real life Meyer Lansky, upon whom Roth is based, was born Maijer Suchowljansky.