I don't speak Japanese, but using Japan's "unofficially" translated Penal Code document, they do not specifically define Pachinko as being allowed or disallowed.
And as you noted with Pachinko, as long as cash is not exchanged directly, that is "enough to circumvent the gambling laws", a practice that "is both understood and fully ignored by all authories everywhere."
But, as in many places around the world, Government Profiteering and Criminal Corruption play into the "historical, monetary, and cultural reasons" you mentioned. So unless you have those ties, and I think you would know, I don't think you will be opening your own Mahjong parlour any time soon.
As this Reuters article mentions, Pachinko's status as an amusement activity and "past links to organized crime" and a "web of special interests involved, not least the national police agency which oversees it" have allowed these private companies to remain cemented into the culture because it is too profitable for those in power to allow it to be removed. But that may change as Las Vegas-style casinos are looking to expand gaming regulations.
The answer ultimately breaks down to the same reasons lotteries are allowed in most states in the United States. As long as the government is profiting, it is going to be ignored.
This article is slightly dated, but is extremely comprehensive in it's examination of gambling in Japan and breaks down the staggering figures as of 2002, and you can imagine they haven't gone down:
- Pachinko, as you mentioned, is exempt from Japanese gambling laws and is bigger than the Japanese auto industry. Each year, 30 million Japanese spend $200 billion, and lose around $40 billion of it.
And though, as the article states, "Japanese criminal law declares unambiguously that gambling is illegal", when you dig deeper:
- Japan’s government-run horseracing industry is three times bigger than any other horseracing business in the world, with nearly $30 billion wagered every year.
- Japan has more professional cyclists than any country in the world. Why? Because Japan runs the world’s largest bicycle-racing betting operation.
- Government-sponsored motorboat races and motorcycle races attract billions in wagers every year.
- The government operates a soccer lottery.
- The government also operates a national numbers lottery.
...and on, and on, with total wagers reaching "on the order of $300 billion/year for legal gambling alone", making Japan the biggest gambling market in the world. Pretty unambiguous.