Uninstalled WordPress and still can't access anything else

I was hired to design an entirely new site for a company, with entirely static pages; their old site was run off WordPress, so when the time came to take my version live, I deleted all the WordPress files from the server and also emptied the database. For some reason now, when I navigate to the homepage, I get redirected to the wp-admin/install.php page, and every other page I navigate redirects to it as well. I looked in the FTP server and there is no wp-admin folder left, nor anymore install.php.

I’ve had to put the old WP site back for now, but I’m wondering how I can actually, most effectively, wipe out WordPress?