I have the same problem. I think it’s due to how Tampermonkey handles when a script is loaded, and how navigation on the wkstats site works.
The navigation bar at the top of wkstats doesn’t trigger a full page reload, instead it only seems to fetch the part of the document that needs to be updated with javascript, and updates the page, history and URL from there. This is why you never see a full page reload when you’re navigating wkstats. However, Tampermonkey and similar extensions only check if a script needs to be activated once a page is loaded, and since this script is only enabled on the projection page, it will not activate unless the initial page loaded was this page. Hence why it does work if you use the link in the OP, since that takes you directly to the projections page, and thus the URL matches what Tampermonkey expects, but doesn’t work if you go there using any other page on WKstats as the first page you visit on the site. You can also manually trigger a full reload of the projections page, after which the script activates too.
@UInt2048 I think a solution for this could be to allow the script to run across the entirety of wkstats, and then add a listener to detect if you’re on the projections page, and running the script if so. I think this should work as a workaround for how these extensions manage when to run their scripts, as they don’t seem to activate scripts if someone changes the URL using the history API.