It's been years since just about everyone stopped using phone numbers for anything so I do see them going away - but not in 2016. People over 60 still "call" and do use "telephone numbers" to do that and they are not all going to die in 2016. Phone numbers will probably be around a decade or two, they will not go away in 2016, they will just become increasingly irrelevant.
One thing that is kind of funny: They appear to be trying. Even my old mother switched to VOIP like 5 years ago because the idea of paying by the minute for calling someone became totally absurd the moment the Internet came around. Now I see "mobile phone companies" offer "plans" where you get free calls and free SMS and some amount of data for a fixed amount of cash per month. Telephone numbers could actually get a comeback! I say could, though, because it's not likely. Nobody I know has been using numbers to call anyone for years and I don't think they will start now.