@ZStoner: That's what currently happens, Kong is testing out new waters with Unity games and my 2 games Big Fun Racing and Bubble Bang are the first ones. Read more about their plans here: http://www.kongregate.com/developer_center/docs/konduit-platform and here: http://www.gamasutra.com/view/news/26515/Interview_Kongregate_On_Launching_Konduit_Capturing_Core_Social_Gamers.php
Of course I understand that, but I can only highly recommand to install that plugin. Unity is the new (and better) flash and there's a lot of cool games coming out using that plugin. Just my 2 cents ;-)
You need to have the Unity webplayer plugin installed to play the game. Only 3mb in size and does NOT need a browser restart. Install right here: http://unity3d.com/webplayer/