The link you posted is for customers who license Flash Player, as indicated on the page. I posted the link for users who do not license Flash Player.
Also, that page is being decommissioned soon. If you distribute Flash Player within your organization, you'll need to apply for a distribution license (free for most use cases) at http://www.adobe.com/products/players/flash-player-distribution.html. Within 24-48 of applying for a license you'll receive an email with the new (unique per license) URL to download the files from.