I think you are wrong. MtGox isn't a financial institution, and aren't registered under Japan Financial Services Agency. There is no category for companies like MtGox. Only banks and other companies involved in payment services, financial instruments, insurance, etc, are.
That's wishful thinking. Of course they're a financial institution. They
take deposits and hold customer money. (And don't pay it back when they should.) If they're lucky, the FSA will just consider them a payment services firm.
MtGox is a place to buy and sell bitcoins. When you transfer money to MtGox is it for the purpose of buying bitcoins. This makes MtGox more like a shop than a financial institution. MtGox never advertised themselves as a place to store money. And they are definetly not doing payment services, since you are unable to withdraw to other peoples accounts. Just your own.
In the US (where Mt. Gox does have a legal presence, in Delaware), they're probably a broker/dealer, and need to qualify as a broker/dealer under US law to deal with US customers. That means SEC registration, audits, insurance, capital requirements, and background checks. Read
"Who is a broker" from the SEC.
I would like to see the law stating they "probably" are. Laws are usually very specific. Either you are or you are not. Their legal presence in Delaware don't make USSAnian laws apply to their Japanese operations in any way. Otherwise it would be impossible for e.g. banks to have offices in Switzerland, where there are strict privacy laws regarding banks and their customers, and in other countries where the government demand that banks release information on their customers holdings.