The definition you linked doesn't seem to support your claim. I have no connection to the EFF, but I'm curious what a better word would be for a short call to action.
This link supports the opposite of davidgay's comment (sources within).
I can't say I've ever heard someone say "Briton" without the adjective "ancient".
It is a very common way of identifying someone as British. e.g. headlines such as "8 hostages, including 2 Britons", "X million Britons now live in <popular location>" are common.