Are these games made with Unity? http://www.needforspeed.com/web/world http://www.joystiq.com/2010/01/29/free-fifa-online-kicks-off-closed-pc-beta-in-february/
Both this tweet from AngryAnt and Wikipedia (FWIW) are any indication, NFSW at least is made with Unity. Don't know about FIFA, as I haven't seen any UT folks comment on it, but it's entirely possible.
I don't see anywhere that it says these are webplayer games. In fact, NFSW specifically talks of downloading a setup file.