Yes, the video is titled "Xbox exclusive content," but the only console specific item so far is a downloadable weapon. Aside from a different colored bow, Final Fantasy XIII-2 has the same cinematic actions and puzzles on both consoles.
Actually, there are three kinds of puzzles called Temporal Rifts in the English version. One of them has players guide Serah as she walks on vanishing tiles. The goal is to collect all of the crystals, but you can’t move backwards since the floor disappears after you move. Another puzzle shown in the trailer is called the Hands of Time, which has players makes players collect crystal that appear when the clock’s hands turn. The final puzzle has Serah connect same colored crystals before time runs out.
Final Fantasy XIII-2 comes out for PS3 and Xbox 360 on January 31 in North America.