Yes...but that was not necessarily a good thing. I hated the original movie, but I think I would have detested this. I will try to sum it up, but I don't feel like wasting too much energy doing so. They put a lot of the stuff from the games into the movie...but it just doesn't really "work" on any level. I don't know if that's because they were too serious, or not serious enough, or if there were tonal issues. It's not necessarily a kids movie, but it would almost have to be for it to be considered a success on any level.
Mario and Luigi are plumbers in New York (called The Mario Brothers for some weird reason), but they're not doing well financially. Mario borrowed money from the mob to pay off their debts, because Luigi keeps doing free jobs for people. He takes care of Luigi after their mother died, but there's a "twist" at the end where Luigi reveals that their mother asked him to watch over Mario, because she knew Mario only cared about money, and would become cold otherwise.
Princess Toadstool is this girl named Hildy in New York that Luigi happens to know and be in love with. She has this mushroom/toadstool locket she lost as a baby when she was left in New York for safekeeping after the Mushroom Kingdom was overthrown, and it was dropped and fell into the sewer. Luigi finds it while they're on a plumbing job, after dreaming he would fine it. Mario wants to use it to pay their debts to the mob. The locket is supposed to have the secret to defeating Koopa inside it, per the wizard Woltan, but when Mario opens it up, Woltan appears and goes "I lied, the power was in you all along". Yeah. It's that kind of a script.
Like the movie, Koopa disguises himself as a man. He's lousy at it, and it's incredibly cheesy, but also kind of funny. He's also allergic to mushrooms. They cause him to shoot fire from his nose (sound familiar?). It does seem like this version of Koopa was going to look more like the one from the game, with a longer snout, shell, etc.
So basically, Mario and Luigi, after the story is set up, they get in a car chase with the mob, and end up in a creepy restaurant serving nothing but frogs, where there's a giant pipe coming out of a ceiling in the back. They hide from the mob in this pipe and end up in the Mushroom Kingdom, in a rolling meadows with pipes with man-eating plants sticking out of them. They have to avoid the plants.
Here they run into Toad, who has been strung up by the inhabitants of the Mushroom Kingdom, to be fed to the carniverous flowers because he is a thief. Toad is described as "a wise cracking anthropomorphic toadstool". He is apparently supposed to be the "bad boy" of the script, as he ends up betraying the Mario Bros to Koopa (with a rocket powered "carrier turtle") so that someone will value him. The Mario Bros rescue him from a trap above one of the flower pipes, and narrowly escape one of those hovering Koopa pirate warships as it heads...somewhere, I can't remember.
Koopa Troppers are in the script, half human, half reptilian, with turtle shells and armor. They go to this part of the Mushroom Kingdom where there are humans that have been subjugated, and from here I just stopped caring about what I was reading.
There's a "Prophecy" about two returning warriors liberting the Mushroom Kingdom.
There's a "quest" that Woltan The Wizard sends them on, promising them that if they succeed, they will return richer than they can imagine (He ends up talking about emotional riches, yeah, it's that kind of script). They're supposed to save the Princess so that the King, who has been in hiding ever since Koopa overthrew the Mushroom Kingdom, can return to power.
Koopa wants to marry the Princess and take the Crown of Invincibility so that he can never be challenged. He makes a show of being nice, it's all very Beauty and The Beast for a few pages. When this fails, he tries to make The Princess fall in love with him by eating a box of chocolates that have a spell on them. With each chocolate she eats, she falls more in love with him, and turns more reptilian.
There are those squishable Goombas, who have enslaved Toad's people. They do not get squished. They're just there, slavedriving the Toadstoolians in one scene.
Yoshii has a cameo when they find his hatching egg, but is never named "Yoshii". In fact, he is instead dubbed "Mario Junior". He runs off as soon as he's hatched, but then returns inexplicably to save Mario from...hell, I can't even remember now.
The Hammer Brothers show up, assassins dispatched to take care of the Mario Brothers, and there's an action minecart sequence.
Mario and Luigi ends up in a cave where you can "buy" treasure with coins they were given, an ice dungeon with the jumping fish, and two castles, as well as the "lava dungeon". Those "falling block creatures" are in the movie, as are the walking bombs, and the cannonball things with teeth. The red flight leaf is one of the things they "buy" in the cave, so there's a flight sequence where Luigi turns into a Luigi with racoon ears and the tail to save himself and Toad from certain doom. The beanstalk is in the movie. Toad and Luigi use it to escape a giant mole in some caves, but we never see the cloud land. Mario and Luigi never become giant versions of themselves.
There are a couple of absolutely ridicilous attempts to humanize or develop the characters. Stupid crap like "Dad gave you this pocketknife, and I always wanted it, so I hate you".
And to my delight and horror, the whole "Sorry Mario, but the Princess is in ANOTHER castle" bit is in the movie, where Koopa's right hand man poses as the Princess, and after revealing himself, literally says "Sorry Mario, but the Princess is in another castle".
There's an incredibly absolutely absurd dance/rap number the Mario Bros do while posing as entertainers to throw Koopa off when they invade his castle.
Like the games, Koopa has like 18 randomly appearing powers.
Believe it or not, the video game's musical themes are sort of worked into the script.
It's really cheesy, and mostly pretty lousy. Early 90's lousy, though, so some people might have liked it. I can't fault the writers for getting as many "game elements" into the script as they did. The story's just not terribly interesting, and it's incredibly predictable. But then, it was based off a series of incredibly predictable video games. I'm probably being too hard on it, actually, considering the source material.