This actually just appears to not work. Chrome seems to do something specific with those pages that stops extensions from functioning properly (not just Zotero). You might want to raise a ticket with them.
That behavior was implemented a few years ago on the Chrome installation and store sites to prevent malicious extensions from messing with chrome installation processes. I doubt that it will change.
https://www.zotero.org/support/reporting_problems#provide_steps_to_reproduce