That is exactly the misunderstanding that I was trying to clarify. Not, "this screen is better for that interface", but the other way around!

Sure, gestures are nice on larger screens too once you get used to them. But why should my uncle's horse's cousin even want to get used to them? The current UI he uses right now works perfectly fine for him. But wait, what's this? A smart watch? No, I don't want one, too fiddly. Not really, you just swipe your finger across the screen to navigate. Aha, cool. I want that on my phone/tablet too!