This mouse has its own wireless receiver with an USB port. The receiver implements a well-known protocol called HID on a computer side; this protocol specifies how devices like mice and keyboards should report the data to the OS.
It does not, however, specify anything about exchanging connection status or battery level, so these features may be implemented by the manufacturer in a specific nonstandard way. Usually vendors do not do that at all; the only hope you may have is an official utility from vendor which comes on an installation CD (or may be downloaded from a website). If there are no such utility, your OS cannot distinguish the causes of not receiving any events from the mouse.