Well, the web does have it's own set of UI conventions: http://www.novolume.co.uk/blog/all-websites-look-the-same/

But the web has it's own set of conventions!

Trying to build a native-osx or native-windows UI on the web gives you a horrible user experience.

This is true. I do not argue that the apps that look & feel differently are not usable, just that they are less familiar and less quick to grasp, which I translate as 'worse'. It is a matter of opinions.

But the web does have conventions that make stuff hard when broken. For example most people expect to see the whole page change when they click a link and doing something else is confusing (such as popping a window or opening a link in new tab by default)

There is no shortage of complaints about websites that do "innovative" stuff and liberties with good ol' conventions.