I just experienced this exact problem in Windows 10 Pro after performing a manual uninstall, by removing all the main program folders and registry entries.
- How to fix -
I managed to resolve it by right-clicking the Hamachi.msi file and selecting 'Uninstall'. Windows then informed me it could not remove the software as it was not currently installed, however it must have removed a leftover registry key that was breaking the installer as it worked fine after this.