The association between what became the modern conception of "Yakuza" and gambling is as old if not older than at least the Edo/Tokugawa period of Japan. What we think of as Yakuza or modern crime was the combination of two samurai era gangs/social groups (depending on how you look at them) called Tekiya (peddlers) and Bakuto (gamblers). It is true that there was a huge focus on gambling in the wake of the war, but that's really only the tip of the iceberg. Organized crime essentially ran all of the black markets (essentially the only markets) in major cities in the wake of WWII, creating a monopoly on all goods bought or sold. This was often in the form of protection money paid to crime syndicates, nominally to protect market vendors from danger but in reality a tax on both their goods and a right to be in the market. But even this pales in comparison to the links between organized crime and politics in the wake of the switch in American policy. Initially, the focus of the occupation was to punish those authoritarians who had committed crimes against the world and in Japan during the war, but as the spectre of communism rose on the world stage this was quickly reversed. Those criminals who had been locked up in places like Sugamo Prison (reserved for many of the worst war criminals, those class as Class A) were not only released but helped back into political office. Often the enforcers they would rely on to keep the peace and break up strikes were a newly reinvigorated Yakuza, who suffered during the interwar years by diminishing numbers. TO be honest this is a hastily done post that doesn't do the subject near enough justice, but a fantastic book on the history and origins of the Yakuza is

http://www.amazon.com/Yakuza-Criminal-Underworld-David-Kaplan/dp/0520274903

which if you have any interest in the subject you should definitely look into.

Also, that book is the source for my post.