SharePoint 2010: Visio Web Access is Not Available on this Site
Problem
Some site administrators have been unable to use Visio Web Access webparts after configuring Visio Graphics Service Application in Central Administration. After adding the Visio Web Access webpart in a page, an error was displayed that says, "Visio Web Access is not available on this site".
Solution
Ensure the following features are activated:
The "SharePoint Server Enterprise Site Collection features" must be activated at site collection level, and the "SharePoint Server Enterprise Site features" must be activated at site (web) level.
Check also the official Visio Services TechNet page: Visio Services runs as a SharePoint Server 2013 service application.