It's called interlacing. You get it at 1080/60i from Canon and Nikon cameras, none of which shoot at 1080/60p ("I" stands for interlaced).
Panasonic G6 and GH3 and Sony Alpha DSL cameras at or above the A57 (but not including the A58) shoot 1080/60p ("P" stands for progressive). Progressive is not subject to the "tearing" you see in the cat video.
Here is an explanation of the difference (see the picture):
Progressive scanning
Nikon and Canon DSLRs with 1080/60i recording are unsuited to fast action video.
If you want to capture fast moving subjects at 60fps, you'll need to do what I did and sell your DSLR for a 1080/60p capable camera like the
$598 Panasonic G6.
It's a darned good 1080/60p action video camera:
[video=vimeo;76875252]http://vimeo.com/76875252[/video]
And a pretty good still camera too:
Flickr: The Panasonic LUMIX DMC-G6 Pool
I shoot Panasonic, and they are terrific modern still and video cameras (I sold my Canon DSLR and my Nikon DSLR is on the shelf).
Hope this is helpful,
Bill