Hey, i thought that unity web player is working under linux as it does under mac, after googling - now i know it doesn't, but one of first links was this how-to: http://wiki.unity3d.com/index.php/Running_Unity_Web_Player_on_Linux_using_Pipelight. This is the best i can do.
Actually, we will have a WebGL version soon, waiting on Unity to resolve 2 WebGL bugs: encryption broken, can't mute the audio!