Why 3 wire CMOS coin battery?
The extra terminal would allow the CPU to sense if such a battery is plugged into the connector. I don't know if that's what it's used for, but that would make some sense. 

Alternatively, perhaps the wire is connected to the + terminal if a rechargeable battery is used, and the trickle charge is just shunted away for the primary cell setup, similar to what @tomnexus is suggesting in a comment. 

If it was for reverse polarity protection, the red wire would go to the middle terminal, so it isn't that.