I found that some laptops use a 3 wire CMOS coin cell. The construction is simple, 1 wire is spot welded to the positive side of the CR2032 and the other 2 to the negative. There is nothing like a sensor of any kind. Why is that so? I can't see the purpose.
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.