Hi @Kalli2000, the first thing to check, is that on the published site on your own server after export, there are console errors, which need to be corrected first, then you can re-test:
Can you check that first? On the webflow site, there are no errors, so the javascript for page linking is running, but it does not seem so on the exported site.
It looks like there was some modifications made to the exported files.