You should charge for it.
[1]: http://www.addictinggames.com/puzzle-games/3dlogic2.jsp
Free sells.
This one has much better controls on the web app, as well.
Does the website demo work on an iPhone (I don't have one to test)?
The standard solution is to give away a bunch of levels for free and charge for additional levels using IAPs.
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.