When you open the installer you might see a popup titled "Windows protected your PC". To allow the application to install, click on "More info" and then click "Run anyway" to run the installer.
If you don't see "Run anyway", the installer might be blocked. To unblock the installer, right-click on the "Earthdata-Download-x64" file in the File Explorer and select "Properties". On the "General" tab, select the "Unblock" checkbox in the "Security" options. Click the "OK" button save the change. After unblocking the installer, double click on the "Earthdata-Download-x64" to start the installation. Click "More info" in the "Windows protected your PC" popup and click "Run anyway" to run the installer.
See Apple documentation for more information about Apple vs. Intel processors.