That Anime was made during the early days of the Mario franchise (1986, I think). Luigi, if I remeraber, wasn't so well defined back then, hence the wrong coloring. Otherwise, yeah, it's an hour long movie about Mario and Luigi traveling the Mushroom Kingdom to (surprise, surprise) save Peach.
Since it is so early in the franchise, the anime took certain liberties to create their own Mushroom Kingdom and dare I say, the results look even more surreal then the video games? Interestingly, it takes the concept the American Mario cartoons would utilized later on in that both Mario and Luigi lived in Earth (or some place that is not the Mushroom Kingdom). They didn't get their via a pipe, but was instead sucked into their TV (or specifically, the video game Mario played). Interestingly, Mario in the Anime is more of a daydreamer who constantly cannot stop thinking about Peach (it's rather cute) while Luigi, before the days of Wario, was a greedy money hog.
The other Mario Anime came out in 1989, based on Super Mario Bros. 3. This one told three short fairy tales using the Mario franchise; two of them based on Japanese tales. The third based on Snow White. The animation is a lot closer to the video games. Also, it had that infamous scene of Luigi coming out of nowhere and kicking Bowser (dressed as the Evil Queen) in the third short, which I declare his crowning moment of awesome.
You can read some more info on these two here.