It seems our fingers have gotten thinner, or more skillful at tapping at relatively tinier buttons now. Look at how huge those buttons are.

I am aware screen size has increased tremendously, even then I think the buttons were still quite huge compared to the size of today's tappable links.

Yeah in comparison OSX Mountain Lion or Windows 8 look basically the same as the modern desktop OSes, while mobile releases from that era look totally different. I suppose it had only been 5 years since the release of the iPhone so there was still a lot of experimentation