Overall, I think this is a pretty decent idea for a reboot - a lot more decent than some OTHER video game reboots at least - but this is extra-tricky to pull off without it backfiring spectacularly. For one thing, a more "serious" story doesn't always mean one that is going to satisfy fans, let alone satisfy people actually looking for a good story. For another thing, a reboot can't be justified with having a more complex story arc if the controls are as basic as - or god forbid, EVEN WORSE!!! - than the original game.
The Sonic series certainly has a good example of a "bad reboot" with Sonic 2006 and Shadow the Hedgehog, where even the more tolerable moments of the stories were overwhelmed by the sheer amounts of badly-flubbed attempts at "being serious", and the gameplay was even worse making the shift from 2D to 3D platforming.
Mortal Kombat (2011), on the other hand, is a good example of a "good reboot": it takes the scraps of the timeline of the Mortal Kombat series, and expands the narrative in ways that makes sense, throwing out curveballs in the plot to show it isn't telling the EXACT same story as the original games, and, on top of all that, the gameplay came a LOOOONG way from the original 1992 arcade release (as Yahtzee himself points out in his review of the game, where he spends the start ranting about the original game based on the "reboot stealing the same name as the original game" joke).
I for one can't speak for gameplay (just different enough from the original that it's not essentially a graphics mod, but not so radically different it totally alienates all the existing fans), but the story hits many of the right notes: the Mario brothers being everyday plumbers from Brooklyn, Princess Peach being another human who took control of the Mushroom Kingdom (thus implying some role beyond "dumbass in distress who gets kidnapped and re-kidnapped to create 50+ sequels"), but I think that the idea to arbitrarily make it "darker and edgier" has a greater chance of making it fail than anything else: the Mario movie is the perfect example, as most of the darker and edgier stuff falls flat since it doesn't add any more substance - it just sucked all the bright, colorful stuff that would appeal to the kiddies and "young at heart" who make up Mario's market, and was still too dumb to be taken seriously by mature audiences.
Instead, the overall tone should be light-hearted, even whimsical - just have it expanded into epic levels. I mean epic in an "epic fantasy" way, where the world overall is expanded in ways that look as bright and appealing as the overall franchise at first glance, but have depth that gets more cynical viewers interested. The environments should have the same asthetics that fans will recognize, but built beyond mere 2D platforming sections with different backgrounds - there should be more to explore, like towns and natural landmarks, and hidden areas that give benefits beyond "lots of coins here". The enemies should be more varied and challenging, but still be consistent with the franchise - or at least, not so dark and edgy they gave players nightmares. The characters should have their personalities expanded beyond their roles in the original games (especially with Princess Peach being competent enough to scrape her way to ruler of the Mushroom Kingdom, and Mario facing more challenge starting out than the completely invincible superhero he is in current canon), but not so they're a total 180 from their old identities. This last bit is particularly important, as this gives all too much room for the writers to shoehorn in cheap plot devices that end up cheapening the character.
So, that's all I got: get the canon of the Mario-verse cemented, make the characters and story more complex than Nintendo's current "graphical paint-job rerelease" trend, but don't go so into grittiness that it turns off the fanbase altogether - and, for that matter, turns off people who know "gritty" does NOT always mean "mature" - and gameplay that's beyond the bare-bones of the original, but doesn't become a clusterfuck trying to be gimmicky.
