I don't understand the live demo

it gave me some ID, but how do I test that some different website can track me resulting in same ID?

or is it only "detect private browsing/container on same browser" kind of stuff?

The "supercookie" phenomenon from a few years ago (when this was created) was that despite using private browsing or deleting cookies, the site id remains the same for the same browser.

It could track you between site visits, at a minimum.