I went through the OEM's web site. IMO, they don't intend to let the end users reprogram the controller in the sense where he would write his own C/C++ code and download it through JTAG. The end user is supposed to use a high level (interpreted?) language and a graphic planner that they provide. They probably think that programs will be small, and that's why they don't provide the size of the memory and how much memory is used up by their own code.
FCC and cost may be the driving forces behind such architecture. If the OEM gives a 3rd party full access to the controller, which runs the stack, the 3rd party might change the radio settings (accidentally or deliberately). FCC would require to re-certify the unit.
Of course, there is another common architecture with 2 separate controllers. One controller (which is accessible only to OEM) is running the Wi-Fi stack. A different controller is completely accessible to a 3rd party. Such architecture wouldn't require FCC re-certification. But the cost of another controller is added.
Hacking this module would be another story. The model number might be written on the controller chip inside. One might be able to look up the parameters (memory, etc) in the datasheet. May be, they will leave the JTAG pads, which could give one access to the controller (at his own risk). They probably will not provide their Wi-Fi stack (at least not for the general public). Finding or creating the Wi-Fi stack could be a challenge.