That's Yugi Moto battling the Pharaoh who was part of him throughout the whole anime series. That's how it ended, he defeated the Pharaoh and sent him to the other side (I didn't watch the series' ending).
The Dark Side of Dimensions movie happens after the series where Yugi is already free from the Pharaoh's soul.
All the main characters in the series are just busy with their regular lives by now (even their previous enemies are here too); but yeah, this movie will be for nothing if there's no action so they've introduced another villain:
His name is Aygami or Diva. He battled Kaiba Sato in this movie:
I personally think it's a good movie, like the original series, which was the only Yu-Gi Oh! series I've watched as a kid (the newer ones aren't that great in my opinion). Have you watched this one?