Their innovation is evolution of WhatsApp past text messages. And in the end, nothing is a true innovation -- most things build on past ideas.
basically they shot themselves in the foot on the mobile market with an half assed implementation, and even today the notification system on skype mobile apps is dumb, especially how they handles balloons (the only app that could do worse on notification balloons is facebook)
whatsapp may not be a cornerstone of reliability, but it has an incredibly frictionless mobile user experience.
The plural is an important side issue. I only have one phone and one public phone number. I'm not sure how many email addresses I have, its definitely more than five but less than two dozen? I do know my broadband provider theoretically gave me an email address about a decade ago that I've never used. I hope no one is sending email to that address...
My mom back in India finds email address and passwords confusing but she immediately understood watsapp and how to send messages to her sister in US.
Skype sometimes hangs on my pc and on the phone. Both my pc and phone have a good configuration yet Skype does not play nice.
Innovation for whatsapp = Simplicity + Reliability
I don't think WhatsApp introduced any innovation at all, its popularity is derived from network effects, together with the questionable practice of using phone numbers as public ID and automatically adding all your phone contacts as chat contacts without them having any say in the matter.