I've installed the unity client (downloaded via Opera), and it seems to work there, but when I switch to IE and visit the same page, it says I need to download the unity client. Is there s specific client for IE as opposed to Firefox/Opera/Mozilla?
It may be an IE configuration issue. There are two things (at least in Opera) that I need to enable for Unity to run - Javascript and Plug-ins. If you hit F12 in Opera you'll see them, presumably enabled by default. It's possible that IE has one or both of them turned off by default. Or it might be a case-by-case basis to enable Plugins.
Try Tools->Manage Addons to see if the Unity plugin is enabled in IE.