of course Gmail isn't an OS, that's not what I meant, but when we use Gmail we're really making more use of the server operating system than the clients, so my point is that it very hard to really say what operating system we're using.
It would be interesting to measure the usage of say posting this comment, how many machine instructions were used at the OSX end, and how many by the various routers (running their own operating systems), servers etc used in the full life cycle of what I am doing.