After installing the magic mouse utilities from recommended site, the miracle happened it works!
Although the software itself is not working, since it cannot run on virtual machine. What!?
But here is the theory.
I used the VMWare Fusion initially, but since it screws up the Windows licensing you cannot use VMWare and Bootcamp at the same time. The Windows gets crazy :-(
So I dumped the VMWare (using it only for Linux) and started to use the Bootcamp instead. It is faster and
better anyway, but here is where the problem with mouse and keyboard started.
It seems that VMWare messed up the drivers, or installs its own, which have now been restored by magic utilities.
Interestingly, the drivers were not restored when I have re-installed them from Bootcamp Assistance.
I assume the magic utils did a rollback to older version or replaced them.