Javascript smoothscroll does not work for some reason

The script works on the links on your live copy as intended, so I believe you mean your videoEnd() function.

The smooth scrolling script that you found only works for anchor tags (<a>).

As window.location.href = "#section" is not an anchor tag, it will not be affected by the script.

What you can do however is take the important bits of that script and use it in your videoEnd() function like so.

function videoEnded() {
    $('html,body').animate({
        scrollTop: $("#section").offset().top
    }, 1000);
}

EDIT:

The reason it is not working for you is because you're browsing the page using the file:// protocol and the script source which links to jQuery is

//ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js

Which uses the // relative scheme, which means that the browser will append the current browsing scheme, turning it into this..

file://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js

Which does not exist. If you specify http:// it will work

http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js