The application isn't using one of the standard installers available on the Internet like Clickonce, MSI, InstallShield, etc.
The software is deployed in form of an .application that uses an online web address to pull the actual installation package. I've searched through the code but didn't find any silent installs as well.
You can get in touch with the developer through the Discussions tab on the official website: https://outlookgooglecalendarsync.codeplex.com/discussions