The screen tearing is most prominent in Crysis 3 Beta (but it happens in all games), I can run the game with maxed out details, but the screen tearing gets pretty bad. Vsync seems to do nothing to fix the problem and only causes input lag.
Normally turning V-sync off, can sort this problem out withing the game graphics menu.
It can depend on the monitor used, and it`s sync V-sync limits the refresh rate of the frame rate of the game to 60Hz so the monitor can cope depending on the brand. but sometimes it can work backwards so give that a try. It can be the cause of tearing in a game.
Use Fraps and run it the next time you play a game that you normally have screen tearing in. I'm assuming that you have a 60Hz monitor, so anytime you're fps goes above 60, you are going to have screen tearing. Then try turning V-sync on, if you are then constantly staying at 60, you should be fine and it should sort out you're tearing. I play with my fps anywhere from 60-80 with vsync always off and I do get the occasional screen tear, but it is totally manageable and totally worth not having the input lag.
Also, i didn't see anything in the video, but Fraps will limit your fps to 30 when you are recording.
I did not see any screen tearing in the video. The remedies for screen tearing are to Turn Adaptive VSync ON and/or adjust graphics settings upward towards higher image quality (and reduced framerate), i.e. turn up the AA/AF.
Also be wary of the Crysis 3 BETA demo, which likely still has a lot of bugs to work out.