Looks like something has gone terribly wrong...
Could you try installing with the following command:
ee site create example.com --wp --user=username --pass=password --firstname.lastname@example.org
Adapt username, password and email address to your needs.
WordPress should come up installed and ready with the set user as admin. No installation page should come up when trying to connect to your site administration pages.
EDIT: please note https://easyengine.io/blog/solution-couldnt-extract-wordpress-archive-error/ if you get an error "Couldn’t extract WordPress archive."