The j2me is just a piece of "it just works".
1) Covers a huge amount of devices. Yep, because j2me, but also because what could be the top-1 competitor, Apple iMessage, can't inter-operate between Apple and Android devices (very stupid tactic, it will get marginalized).
2) Does not require an account, so it is not bound to Facebook, Twitter, ... You may ask, what's the problem with having an account? That you capture in your use base non-social people. Hey mom, put this in your phone and we'll exchange messages for free.
3) Because it just works and is not bound to a specific social network / company, people see it as SMS that is both free (hugely important because of stupidly overpriced SMS are, and especially, were). And... an improved version of SMS because MMS are totally a fail: limited, costly, lame.
4) Add to this business smartness behind that: old users don't pay for premium accounts, no ADV, resist to the temptation of fixing what is irrelevant for the mass of people (security) if this impacts in any way the product aspect (no account, trivial recovery of the account if you change phone).
5) Add to this product/technology smartness: don't archive messages server side so the service runs with 1/100 of resources. No huge scaling issues.
So this is just a very very very well executed product, that was able to provide what users wanted, and this is why they did a 16B deal, not for the j2me app, every successful business is a mix of a number of critical things.
The ground that made this possible was the incredible situation where on the internet era you had to pay 10 cents to exchange 160 chars between two phones.