Dont they dive in a part of sea that is international, so no rules apply?

The companies are incorporated in some country however. And ships that go out to sea must be flagged under some country, and those ships have to follow the rules/regulations of the country they're under.

And their failures cause those same countries non-trivial amounts of money.

Consider the Coast Guard and Navy efforts for this latest event.

According to the news I read, Titan did not need to be classed/certified because it didn't launch from any port. Even if the mother ship did. I'll try to find the citation.

Why? You are comparing ships, which have passengers whose goal is to get somewhere (not necessarily be on a ship) and don’t self-identify as final-frontier risk takers with subs which are the exact opposite. Nobody takes a sub as regular or holiday transport. The point of the (non-military) sub is to go where almost nobody goes, where only a sub can go. And you don’t leave the sub.