HI Andy,
Check to see if you are running into mixed content issues, (using a mix of http and https). Sometimes microsoft browsers are configured to allow mixed content whereas chrome by default blocks the content. To determine this, check the following:
1. When opening the map viewer, ensure that it is loading via https. If you see http in the url, modify the url and reload the map. Then try to add the vector tile layer.
2. When opening in chrome, press f12 to bring up developer tools. Click on the console tab and see if there are any errors. If there are, check to see if the errors indicate that there are mixed content issues.
3. Check for errors (red x's) in the right hand corner of the URL loader to see if you are receiving an error message about secure content not loading.
You should be able to load vector tiles in chrome, so let us know if fixing a mixed content issue resolves the issue.
Kelly