I looked up the video of the championship game because I was curious too, but they go so fast it's hard to really follow - and I don't think any of the psychic pokemon in that deck were played. I believe it was only Yveltal, Darkrai EX, and Shaymin EX
If I had to guess, the psychic pokemon may be there just for their abilities - HoopaEX allows the player to get up to 3 pokemon-EX from the deck on the turn it's played, and Garbodor cancels out the effect of any other pokemon's ability as long as it has a tool card attached. ShayminEX itself may be there mostly for it's ability as well - when it's played, you can draw until you have six cards. The strategy seems to be to get Yveltal and DarkraiEX out and powered up as quickly as possible - I'd be interested to hear the opinion of someone more versed in competitive play than I am though
