Minecraft is a videogame only in the loosest sense. Digital sandbox is a more accurate description. Players are free to construct buildings and objects out of 3D cubes, polygonal Legos of sorts. The program, which is available for PCs as well as Apple (AAPL) and Google (GOOG) phones, eschews the ultra-realistic, blockbuster graphics of contemporary computer games. With its pixelated, blocky textures, Minecraft looks like a relic from the Atari era. In one mode, players must gather resources during the day and fend off monster attacks at night; in another, they are free to create whatever they like.

The game’s difficulty adds to the old school flavor. The learning curve can be punishing. In lieu of a manual, users are encouraged to buddy up with a “mentor” to show them the ropes or crawl user forums and web videos for tips on everything from scavenging for materials to building huge monuments. “The same thing that draws people to Minecraft is the same thing that draws people to make their own music videos or to try to sell their own crafts on Etsy,” explains Leigh Alexander, editor-at-large for game industry web site GamaSutra.

MORE: The problem with Zynga’s growth

This freeform gameplay has generated a robust culture, with players creating and sharing their designs online. A common internet meme over the past year has been “xyz re-created in Minecraft,” from Frank Lloyd Wright’s Fallingwater to Harry Potter’s Hogwarts. Although the Mojang team says its largest demographic set is under 15, Minecraft’s users range in age from 9 to 70, casual gamer to seasoned veteran. To date, the game has more than 25 million registered users, 5 million of which paid upfront for a premium version with additional features.

That has translated into a real business. The company reported $80 million in revenues — and $13.5 million in profit — through the end of 2011. Large publishers have come knocking with acquisition bids, rumored to be worth close to $1 billion. And rockstar entrepreneur Sean Parker flew the developers to London for a party hoping to woo them as a future investor.

A good barometer of how rapidly the game has grown in popularity is MineCon, the annual Minecraft convention. Its first gathering in Bellevue, Washington two years ago was a low key affair attended by Persson and around 50 other devotees. Last November, MineCon drew 5,000 fans, packing the Mandalay Bay Hotel and Casino in Las Vegas. “Going from your small offices [in Sweden] to MineCon, and meeting these people, that’s when we realized how big Minecraft was and what kind of impact the game has made,” says Manneh.

MORE: Is Pinterest the next Facebook?

Minecraft’s success is largely due to Persson, its creator, described by industry insiders as bright with a sharp wit. He worked for some four-and-a-half years as a programmer for King.com, developing casual puzzle and shooting games with names like Funny Farm and Carnival Shootout before jAlbum. Persson never anticipated becoming a millionaire, let alone an industry luminary. Still Notch, as he calls himself online, already commands a sizable influence. More than 640,000 people follow his frequent updates on Twitter, while nearly 112,300 track him on Google+. (Persson declined to comment for this story.)

Indeed, just as appealing to fans as Minecraft itself is Persson’s anti-establishment persona. He is above all a programmer, but he hasn’t shied away from controversy. In an interview with an industry trade publication last year, Persson said he may have quashed Electronic Arts (EA) boss John Riccitello’s potential acquisition hopes over lunch. When the CEO of game maker OMGPOP, which was recently acquired for $210 million by Zynga (ZNGA), made disparaging remarks about the one employee who did not make the move, Persson came to his defense. He shot back on Twitter, “You’re an insane idiot.” And when a fan admitted, also via Twitter, that he couldn’t to afford to buy Minecraft, Persson publicly recommended he pirate a copy. Instead of pocketing nearly $3 million in dividends last year, he gave it back to Mojang employees, bolstering his Robin Hood image.

More importantly, Minecraft’s parent Mojang is bucking two of the biggest trends in games. It is unlike casual game makers Zynga and Rovio, pumping out low- and no-cost titles people play as diversions on the subway or at work. Nor is it like larger game firms EA and Activision (ATVI), which operate much like Hollywood studios, investing tens and sometimes hundreds of millions developing complex titles like Call of Duty. With its idiosyncratic approach, it is most like the old Blizzard, the small Irvine, California studio that wound up creating World of Warcraft, one of the most profitable franchises in history. (It eventually merged with Activision in 2007, an $18.9 billion tie up that created the world’s largest game maker.)

MORE: So you’ve got a blockbuster iPhone game. Now what?

Mojang is looking at ways to expand, which includes everything short of being acquired. That includes placing its bets on an all-new unrelated adventure game called Scrolls, which will initially roll out in an invite-only “closed alpha” in the next two months. And earlier this week, Persson announced another game, dubbed 0×10^C, an ambitious-sounding multiplayer space travel game.

Key to maintaining overall growth of Minecraft itself will be exploring opportunities that make sense for the game, says Scott Steinberg, head of business consulting for the video games firm TechSavvy. Mojang has been approached to develop the game into a TV show or film, although the company hasn’t committed to anything yet. A version of the game is headed to Microsoft’s (MSFT) Xbox Live this May. And merchandise, which generated nearly $1 million last year, will get a big boost later this year when an official Minecraft-inspired Lego set arrives. For Persson and crew, that is likely only to be the beginning.