The best theory I've heard is that he was influenced by his older self in that moment. Stars have been shown to represent both worlds and individual people in the Kingdom Hearts universe, and the Young Xehanort in the intro was looking at a purple (this color likely symbolizing some kind of powerful dark force) star, representing Master Xehanort. From there, he's inspired by his older self's machinations to move the peices a certain way. One that mirrors every major event that happened in the series thus far. This is why we see flashes of Xemnas and Ansem, for example, when he moves their corresponding chess peices. He's in a sense, recreating the major events of the series (note that he likely doesn't realize he's doing this, but those events are still etched in his heart after his time traveling in DDD and KH3), all prompted by looking at his own star in the sky.
One last interesting fact:
- He's playing chess alone, & at night time during the opening. This is likely a practice match against himself so he's prepared for his big face off against Eraqus the following day. Remember that he nearly beats Eraqus by applying the same set up his older self used in the end of KH3, and Eraqus, in tern, triggers the lights from the past (again, mirroring KH3). So it can be presumed that he's still being somewhat influenced by his older self/time traveling experience when he plays chess with Eraqus.