Your initial assumption is heading in the right direction. You can use Zen Cart as a cart with Google Checkout. But then you take a wrong turn.
The normal approach isn't to integrate Zen Cart into a website, but to build a website using Zen Cart. Google checkout is an add-on module which can be downloaded from
here.
Most users will have little interest in how it is structured, just the ease of installation and confirmation that it works. If you need more than this, then it is easy to download it and perform your own evaluation.