There is a solution, but I am not 100% that it will work with all older hardware.
I am running Windows 7 on a dell m3800, so the problem is NOT the OS.
As some other posters have noted, the Arch Touch Surface mouse uses the latest version of Bluetooth. "LE", "4.0", whatever you want to call it. In my case I simply needed to update to the latest Bluetooth drivers. Once the latest Bluetooth was installed, windows was able to detect the mouse, install the latest mouse drivers and get everything working.
I am NOT using a separate USB Bluetooth dongle, just the Bluetooth native to the laptop. I suppose it's possible that someone with an old laptop/USB dongle would need to get a more recent one... I have no idea if the updated Bluetooth driver is backward comparable with older hardware.
But, in my case, updating to the latest Bluetooth drivers did the trick.
This worked for the Arc Touch Surface and Arc Touch Bluetooth versions of the mouse.
Hope that helps.