What you are describing (and what your screenshot shows) is the Mobile (non-Flash) player which is used for mobile devices which do not support Flash and for browsers when Adobe Flash Player is not detected (either not installed or not enabled).
In IE9 on my PC, your gallery is displayed using Flash but in your IE9 browser, the gallery is displayed using the Mobile Player.
If you do, indeed, have the latest version of Adobe Flash Player installed in IE9, then it looks like it is disabled.
You can check this by going to 'Tools -> Internet Options -> Programs -> Manage Add-ons -> Toolbars and Extensions' and ensuring that 'Shockwave Flash Object' is enabled.
(Also, remember that IE9 requires a different Flash Player installation than Firefox.)
SimpleViewer Support Team