Behavior:
It is not possible to use any of the ClickOnce applications in HTML5 Viewer.
Solution:
In Windows Server 2008 and 2012 the option "Internet Explorer Enhanced Security Configuration (IE ESC)" is enabled by default.
If this option is enabled it is not possible to use any of the ClickOnce applications in HTML5 Viewer.
In order to be able to use ClickOnce applications you'll need to disable IE ESC in server manager > Security Information > Configure IE ESC