Hello,
After some verification, it appears as the package from the marketplace does not include the ZIP Archive package for Compute Engine. ZIP is included in App Engine as part of the PHP Runtime.
If you are using cPanel on GCE, and click on the icon labeled "PHP PEAR Packages" (in the Software section). Next, in the search box (underneath the "Find a PHP Extensions and Applications Package" heading, type in "zip" and click the Go button. On the next page, you should see a listing for Archive_Zip - simply click on the Install link on the right hand side.Then you would need to select your PHP version and then select the zip module.
If you are not using cPanel on GCE, you would need to manually install the Zip Archive. The following post[1] on Digitial Ocean's community forum will guide you further. You will need to adjust the PHP version to your current version.