There's also a solar panel, but I agree it seems crazy high.
To be fair, the main thing is that they are actually getting adopted and used, integrated into village life. It's common to spend a lot of money "helping" people, with no long-term benefit to them.
I don't think these are a bad idea. On the contrary they're actually pretty cool and I wouldn't mind having one as a 1st world american for camping trips and the like. It would beat trying to use a strong flashlight and a white 10 gallon bucket as an impromptu area lamp.
I would bet within a year, some clever entrepreneurial person where these are being used will start converting old car batteries, flashlights, some old tubing or wood and junked mopeds into these. Sells them for $30.
And then decoupling the panels and building centralized solar powered charging stations out of used 120W solar cells (on ebay, $120 even 12v!) and sells a "charge" for $.10 or whatever the local market can handle (or a village can buy one for $200).
An even more clever person could turn a pump, wind turbine or a see-saw into a charger/generator and top these things off while the kids play.
The led and battery, from what I understand, seems to be imported as a single module from a manufacturer that produces public street lighting, hence the high price.
The BOM on this is probably under $50 tops.