It's not a question of possible or impossible. With an external genlock or video mixer, what you want to do is 100% possible using the Pi to generate video. Unfortunately, external professional quality genlock / video mixer systems cost significant amounts of money.
Another option has been pointed out to you, it's a video mixer shield for the Arduino. Whilst the Arduino is less powerful than the Pi, it has the benefit of being available now, is certainly capable of producing the sort of graphics you want, and is significantly easier to interface to the external world (I assume, given the video you've posted, you want to interface as well). Not to mention that it has a plug 'n' play, ready-to-go solution for doing exactly what you want, and at a price that is more than reasonable.
That gives you 3 choices, pretty much:
1 - get yourself an external video mixer
2 - go with the arduino + video shield solution
3 - design your own video mixer similar to the video shield.
I don't want to buy an expensive mixer, otherwise I wouldn't have asked you.
I asked on the forum because I wanted to know if Raspberry Pi could be synchronized with an external live video signal. I mean : able to start its odd/even frame whenever I want.
I can make an arduino-like, I already did it. It works fine. BUT : process power I need is not enough on that type of processor/µC ! That's WHY I'm interested in RaspberryPi.
One solution is to use Raspberry to make graphics and write "screen objetcs" on a buffer shared with a low cost mixer (Arduino, Microchip, MAX7456, and so on) that mix with the live video.
THAT SOLUTION (which can be done) simply synchronizes those two video signals.
But this "hardware mixing" solution is more complicated than simply synchronize raspberry video signal...