This battery was sent by Kim Sleep, who's sent a few other items in the past. It's a rechargeable PP3 style 9V battery that has a built in micro USB charging connector and a generous lithium battery that gives the unit a capacity of around 400mAh at 9V.

The use of a boost circuit to step the voltage up to 9V means that it remains at that level for the full discharge until the lithium cell's protection circuitry shuts it off.

When I had the unit open I intuitively resoldered the connection between the two parallel cells, as it looked a bit dry.
Russ Wigglesworth sent a link to a full battery test where one of two batteries had only half capacity, suggesting that the solder connection between the two cells was not intact.
http://budgetlightforum.com/node/51493
If you have a battery and it seems to have half capacity I'd recommend opening it in a half charge state (to minimise cell voltage differential) and very carefully testing both cell voltages. If they are different, then the cells may not be connected together properly. They will need to be at a similar voltage before resoldering them.

If you enjoy these videos you can help support the channel with a dollar for coffee, cookies and random gadgets for disassembly at:
http://www.bigclive.com/coffee.htm
This also keeps the channel independent of YouTube's advertising algorithms allowing it to be a bit more dangerous and naughty.