Correct in that the animated film is based on the video game and not the actual poem. (Funny enough, the film takes several liberties with its source material-at this point it was almost a re-imagining of a re-imagining.) It was a game a lot of people wrote off because they thought it to be just a God of War clone-which I admit it totally is. But it was a good GOW clone. Much better then GOW 3 which was I played about the same time. Dante's Inferno had much better art direction and a protagonist I could actually sympathize with, as apposed to Kratos, whom at that point I had lost any sympathy I might have once had for the character.
The film in question I thought was in poor quality. I'm not a big fan of anime to begin with, but if Iwas this would not be a film I would use to introduce people to it. There where segments that just ugly, poorly done, and even a few scenes where the animation was reused (leading to some odd lip syncing moments). I know the idea was that it was several different directors doing different segments-but this lead to some wildly different looks that was jarring, and in some cases kind of funny. Like when Dante is in one moment an almost fully armor clad knight and in the next is a bear skin wearing, long haired barbarian.
And yes, I have read the original poem, long before I ever played the game or saw the animated film.