Could you try running the installer as administrator? (is probably an option when right-clicking the msi file)
Alternatively, open the Command Prompt (Admin) and execute the installer as follows:
msiexec /i "tiled-0.16.1-win64.msi"
If this doesn’t work either, try the non-installer based distribution. This is currently only available for the snapshot builds and you’ll need 7-zip installed. You can find them at https://update.mapeditor.org/snapshots-win/.
Ok. I’ll just note, that being logged in as admin doesn’t mean that everything you run is running with administrator privileges (fortunately).
Nice. Still, it’s strange that this was needed. Normally, the installer asks for administrator privileges when it is run and the error message you received was also weird. I hope not too many people run into that.