If you just want to resize buttons, you can do this with simple CSS.
In your HTML code (on the player you posted), find these lines (below), and you'll see there's a bunch of <button> tags. These are your player controls. And by looking at the code you'll be able to tell which is which since they're pretty easily identified.
For each button you want to modify, you can add a CSS class to them. In the example below I've added a class of "new_button" to the play button.
Now all that's left is to actually "style" that button... for example, if you wanted to make it HUGE you could do this: (This goes in your CSS section)
Again, this will make a HUGE button (as an example), and you'll probably have to modify your HTML elsewhere to compensate for such big buttons, but this will do the trick of resizing them.