Q: No eBay API: How does this work?
A: All is explained in a link there on the page that you were looking at. Here's a direct link - https://go.skugrid.com/sku-grid-ebay-repricing-options/
You have different options you can set up to have your items updated.
1. Manually do eBay File Exchange
2. File exchange + Chrome Extension to help automate that process
3. WooHosted
4. Multi-channel management --> which would be eCom Syndicator that you can set up to automate the revision of your items