It's not that one billion new users will bring 15 billion new devices.
It's that a) there will be one billion new users. And b) these users, plus the existing users, will increase the device-count by 15 billion.
Thus, if there's a total of 3 billion users (including the new billion), then each user needs on the average 5 devices more that are online-capable than they have today.
This seems not at all unreasonable, but depends a bit on the interpretation of "next few years" offcourse.
At the moment, we're mostly talking computers and infrastructure. (servers, laptops, routers, desktops) but in the western world, other devices are coming online now.
TVs come with internet-access built in. (atleast DLNA, sometimes more) Mobile phones come with internet as a core function. Cars hook up trough the mobile-phone. Radios become internet-radio-capable. Printers get their own ip-address and hook up to the wlan at home. home-security-systems become accessible over tcp/ip. Automation means tcp/ip may become involved when you press a *lightswitch* in your home. Digital cameras get wlan-access, in order to make the pics downloadable without needing a cable.
None of this is the future. This is tech that's at the early-adopter stage in the rich parts of the world NOW. I ain't counted, but I'm positive there's in excess of 25 devices in my home that speak tcp/ip, and if we include the devices I and my wife use exclusively at work, you can add another handful.
We're not typical - but I find it entirely plausible that when we've got probably 30 devices TODAY, that the average western rich-person will have 10 of them inside of the decade.
Now, not all of these devices are nessecarily globally reachable, some of them live on their own internal network that may or may not be connected to the global internet, but even when it is, there's typically NAT between, so they all appear as a single ip on the net. Nevertheless, if a device is capable of pinging lwn.net, I think it's reasonable to say the device is online.