As mentioned here, changing the ringtone of the Web Client is not yet available. However as my colleague mentions: "we will consider it in our future plans as the Webclient will be our main focus and it will be getting more features over time."
Thanks for the info. Yes I think more configuration options will be appreciated. Do you happen to have any ETA on this as I see that post was from Feb.
I don't have an ETA for you right now, but it'll definitely be announced via our blog when updates are made. I'd suggest keeping up with the latest posts as I'm sure you already do.