Actually I think it's a LiPo (lithium polymer) battery which is cheaper and not as good as Li-Ion. I can't remember the exact differences but I think one of them is that Li-Ion can be charged more often without deteriorating.
I don't think its a true LiPo pack. If you read the Wikipedia article on the subject there seems to be two types. The type with a dry polymer electrolyte (LiPo), and the type in a flexible polymer casing/pouch with a liquid or gelled electrolyte. The latter being no different to Li-ion packs.
The general manufacture of Möbius cameras may mean that sub par batteries have been used - unfortunately I don't think you'll find a better battery to fit the form factor and case of the camera. If you want to extend it further, you could investigate using a USB power bank as an extended battery.