Alright, I don't know the title of the first movie, but I don't think it had much of one anyway.

I've seen this movie subbed myself, and honestly, without seeing the first whole series,
you think 'What's up withthe art style?'

Well, I'll tell you the point of this movie, or at least, what I think the point is.

The point of this movie was to bridge the gap between Yugioh, Game of Darkness
and Yugioh Duel Monsters (The one airing in US and Japan).

The Games of Darkness series was both darker, and yet lighter than the current running series
We know this because of Shonen Jump, since we get a glimps of the original series.
Not everything is the same in the manga and anime, but that always happens.
Yugioh is currently totally running off form the story line of the manga, which they've already discovered Yami's name, and are in Egypt.

But anyways.

In this movie, a kid named Shin gets the extremely rare Red Eyes Black Dragon.
He's weak and even more pathetic than Yugi in ways.

Well, we find the Yugi gang (Which exists of Yugi, Jounouchi, Honda, Miho, and Anzu) at a gaming place where Anzu works. yugi's teaching Miho how to play when there's a commotion outside of their booth.
Everyone looks and it's Shin surrounded by 'friends', who are asking him about the Red Eyes.
Shin runs away and Yugi is a bit saddened.

The next day Yugi gets an invitation to a tournament hosted by Seto Kaiba.
Yugi takes it and doesn't know if he wants to go.

the next scene is of Yugi and Jounouchi walking down the street, when they see Shin being bothered by a few of Seto's lackeys. Well, naturally Jounouchi gets mad and takes out one of them and tells Shin and yugi to run.

yugi and Shin run into an alleyway and Yugi talks to Shin on how he shouldn't fear dueling, and some other things.

Suddenly, one of the guards find Yugi and Shin and he beats them up, taking the Mill. Puzzle and Shin's Red Eyes.

Jounouchi finds them and he goes off to find the guard. Yugi and Shin talk for a moment and then run off after Jou.
Once at the tournament, Yugi and Shin find Jounouchi being beaten by a guard. Once the guard leaves, Jounouchi smirks and takes out the stolen Red Eyes.
Jounouchi yells at Shin, and Shin begins to run away, but yugi stops him, in the process making them spill their decks.
As they pick up cards, Jounouchi helps out Yugi and gives him an extra card.

We next see inside the stadium, as Dinasour Ryuzaki (Rex Raptor) runs out crying (haha, ugly). Seto's sitting there, waiting patiently for a next opponent.
Yugi comes in and Seto tosses him his puzzle. Yugi takes it and puts it on.
Now, there's a different way in the original series that Yugi and yami switch. Yugi's shadow would normally be lengthened, and the shadows 'eyes' would open, and the mill. Eye would be in the shadow's 'forehead'. Then it would fade into Yami and the b/g would go back to normal.
I kind of like the original way of their mind shuffle, but oh well.

And so, Yami and Seto duel using Kaiba's latest dueling system (It acts a lot like his Duel top thingies from Duelist Kingdom).
After a while, Yami finds outthat he had Red Eyes, but he can't use it unless Shin wants to fight.

After a short speech from Jounouchi, who acknowledges 'Mou hitori no yugi's presence, Shin decide's to help, and Red Eyes comes forth, beating Kaiba.

Good day.

And so, Yami, having won, Jounouchi and Shin run down to the stadium floor, and Jounouchi sort of glomps Yami.
Watching this scene in slow mo will be sure to freak out out, yet make you laugh hysterically at Yami's face.
And this, is basically where it ends.

There's supposedly another yugioh Movie coming out in August (In japan I think). I know nothing about it though, and neither does anyone else really... But I think WB asked the makers to create it... so who knows...