It's not really that savvy people would be switching away; it's that non-savvy friends/family of savvy people who read this article now will have a slight negative connotation to those product names, so if their savvy friend/relative tries to convince them to switch to either of them, they might say no for stupid reasons.
This is the point of the majority of propaganda, really: it's not to convince the people who know anything about the issue; it's to prejudice the people who don't, so that it'll be harder for the people in the know to communicate the facts to them.
In particular because the App Store features not only the usual suspects (Skype, Allo, ...), but many other somewhat random apps (Gonzo, BabelNet, Kissapp, 5s, ...) promising encrypted chat, and people might think, "hmm, WhatsApp and Signal are insecure, it says so in the NY Times, so let's try one of these"
It already happened with Whatsapp and the Guardian's irresponsible reporting. Organizers and protesters switching to unencrypted messaging or even SMS, because of the perception that Whatsapp was hacked. Someone savvy enough to use end to end encryption may be someone who values privacy, but there's not reason to assume they are also someone who is themselves a security expert. The point of apps like Whatsapp and Signal working to make end to end encryption easy for the average person is to increase encrypted messaging use, not make everyone a security expert.
This is the point of the majority of propaganda, really: it's not to convince the people who know anything about the issue; it's to prejudice the people who don't, so that it'll be harder for the people in the know to communicate the facts to them.