Plugin update didn’t include some files

Last week I installed an update to one of our mission-critical plugins: our main payment gateway. Some PHP files that are in the plugin did not get copied to the site’s plugin folder, with critical effects on gateway functionality. I don’t think any data was lost.

Can I rerun the plugin installation and get the missing files that way? If that doesn’t work, can I simply manually copy the missing files into the site plugin folder?

The page I need help with: [log in to see the link]