You do not. My brother uses it heavily on his WiFi-only iPad Mini.
When I first bought WhatsApp, I bought it in iTunes on my Mac. I only had iPod touches and iPads at the time, and it wouldn't sync the application to any of them. I seem to recall that I tried to follow a direct link to the App Store entry from Mobile Safari, and it said that my devices were incompatible.
I had to sideload the WhatsApp.apk on to my Nexus 7 Wi-Fi.
Then you receive your activation code on your phone and tab it in on your tablet.
It works perfectly well.