I've discovered Windows 10 Security doesn't always notify you when Controlled Folder Access blocks an executable. 

Try the following:
Attempt to run the installer, and provide permissions to any popups. After this nothing may happen.
If Controlled Folder Access does not notify you, go to its settings and look among "recently blocked" apps to whitelist.
If you run the installer a second time, it should at least get to an installer interface that allows you to choose an installation folder.

There's a chance that the installer will run a second executable that also needs to be whitelisted before the Itch.io app can run.