I just found this website which seems to be developping a browserFPS that seems to be quite advanced (technology-wise) and which could lead to an online fps played in the browser.

EDIT: I forgot to mention there was actually a multiplayer mode! Just go under the network tab in settings and set yourself as a client, refresh server list, select one server and there you are !

It requires Flash + Shockwave, playabe under IE and FireFox