Based on my reading of the BT878 datasheet
( ** LINK ** ), the chip is using a 1 of 4 input multiplexor. IOW it captures from one video input at a time, and commands from software tell it which input it should be using. See page 107 of the datasheet (which is page 119 of the PDF file). This just reconfirms my belief that the various "4 cams at once" security softwares are just driving the multiplexer in a fast round-robin of inputs - thus not truly capturing from 4 cams at once but actually "time-sharing" one BT878 between 4 cam inputs.
So, I expect what you are going to find is that your card turns up in AbelCam (and in Windows device manager) as ONE video device (the chip), not FOUR devices (the inputs/cams). That isn't gonna work for what you were wanting to do. If you feel brave, there is probably a third-party driver for BT878 cards out there somewhere that implements the multiplexing round-robin at the kernal level and presents 4 "virtual" video devices to the WDM. Maybe.
Also have a look at this card
( ** LINK ** ) which clearly says it CAN deliver 4 cams simultaneously. By the looks of the picture I'd say it has 4 BT878s on-board plus a fifth large chip for something or another.