Who says you need completely novel gameplay mechanics to charge money for an app? Surely more polish, hand-built levels and an app are sufficient. Whether OP would make more on ads or IAP remains to be seen, though. An IAP to get more levels would be a good way to hook users.
This only works if their site gets views and the free demo gets plays. In my experience, apps in the App Store are primarily found through the App Store, meaning potential users won't hit the site first to try the demo.
The standard solution is to give away a bunch of levels for free and charge for additional levels using IAPs.
I'm guessing that demo is getting a lot of plays right now and they should capitalize on the hype that's being built.
Relying on the App Store is a good strategy for development firms that cannot build their own hype. So far, I'm guessing these guys are doing an okay job.
But I have zero data on any of this, hopefully they do and are acting appropriately.
We felt that out of the gate making it free to download was our best chance for success, but who know, if we start getting into A/B testing in the future, we may find that keeping the game free in the browser and charging for app store installs is the way to go.