Microsoft CEO Satya Nadella. Business Insider When Microsoft CEO Satya Nadella first took the job back in early 2014, he laid out a bold vision for the company: "mobile first, cloud first."

At the time, it didn't seem to mean much.

But in the last year and a half, Microsoft has undergone a radical shift, slowly but surely transitioning into a company that doesn't care what device you use, so long as you're using a Microsoft app on it. It's pretty cool.

Now, with a big update to the Xbox One console coming this November that adds Windows 10 at the core, Nadella's vision is coming to Microsoft's gaming business.

"It's not really hard to think about that [vision] with games," says Xbox Group Product Manager Peter Orullian.

It comes at a critical time for Microsoft, as it looks to close the gap between the Xbox One and its leading rival, the Sony PlayStation 4. Good thing it's arriving just in time for the holiday shopping season.

Satya's vision

The real crux of Microsoft CEO Satya Nadella vision is the idea of putting the user first. Want to use Office on an Android tablet? Fine. Want to run Skype on a Mac? Cool.

What's important to CEO Satya Nadella, he's said over and over, is that users love Microsoft. And cloud-based tools like OneDrive and Office 365 make sure that a user's data is consistent, from a Microsoft Surface Pro tablet to an Apple iPhone.

But gaming is a major part of Microsoft's business, too.

This limited edition Xbox One holiday bundle is themed around the "Halo" series, in time for the forthcoming "Halo 5: Guardians." Business Insider/Matt Weinberger

There's the Xbox line of video-game consoles, which grew from a concept for a living room PC into a major brand in its own right. And the Windows PC has been the platform of choice for super-serious gamers for more than 20 years.

For a long time, the two have been totally separate. But in November, there's a big change coming to the Xbox One, putting a version of the new Windows 10 operating system at the core of the console. That's the same Windows 10 that runs on PCs, tablets, and, soon, with Windows 10 Mobile, on smartphones.

Master Chief and company are a lot more acrobatic this time around. Microsoft

"This means we now have one operating system on all Microsoft devices," says Orullian.

This update does some cool stuff, including a brand-new menu system for Xbox One that reduces the reliance on the Kinect sensor to get around, plus backward compatibility with a lot of Xbox 360 games from the last generation of hardware.

But in the bigger picture, it means that the door is open for Microsoft to serve gamers the same way it's serving businesspeople, students, and other people who get stuff done.

Phil Spencer, head of Microsoft's Xbox Division. Kevork Djansezian/Getty Images

And under the leadership of Phil Spencer, Nadella's appointee to lead Xbox and gaming across the whole world of Microsoft, that plan is working. And Nadella and Spencer are working together to make gaming into a big part of Microsoft's sales pitch to the world.

"He is fully on board with gaming," Mike Lavin, senior global product marketing manager for Xbox Live, says of Nadella.

Crossover appeal

So far, most of Microsoft's transformation has been focused on productivity.

The Office 365 cloud-productivity suite, in particular, is growing beyond its Microsoft Word/PowerPoint/Excel roots, and into a set of useful apps and services that work on Windows, Mac, iPhone, Android, and, oh yeah, Windows Phone.

For gaming, the equivalent is Xbox Live. Microsoft is pushing Xbox Live as the center of your gaming life, across PC and video game console, just as it's pushing Office 365 as the center of your working life.

"It's the glue," says Lavin.

The Xbox app in Windows 10 is like Facebook for your gaming life. Business Insider/Matt Weinberger

The Xbox app on Windows 10 has a lot of nifty features: You can use it to take and view screenshots and recording from within any PC game. You can use it to view all of your Xbox Live friends, and see what they're playing, either on the console or on the PC.

Best of all, you can actually use it to stream the Xbox One across your local network, letting you play console games right on your Windows 10 PC.

It means that from any Windows 10 PC or tablet, you can launch any of your games, Windows or Xbox. And with the Xbox Live service underpinning it, it adds a really sticky social layer that keeps your achievements and friends list consistent between the two.

"It doesn't matter where you are," Lavin says.

"Everything will be unified at some point"

Going forward, putting Windows 10 on the Xbox One is just going to break down even more divisions between the two.

Microsoft has already announced that Cortana, Windows 10's personal digital assistant, is coming to Xbox One sometime next year.

And the Windows Store, Microsoft's app store, will also be combined at some future point with the Xbox's existing digital game store. The advantage there is making it easier for developers to make a game once and sell it everywhere.

With the Xbox app's streaming capabilities, even relatively underpowered computers like the Surface Pro 4 can play new release games with ease. Matt Weinberger

Plus, the Windows 10 update to Xbox One is going to make it easier for games to enable multiplayer gaming between the PC and console, which has long been a technical challenge for all the major platforms. Microsoft-published titles like "Gigantic" and "Fable Legends" for Windows 10 and Xbox One will be the first to support it.

The theme here is the gradual blurring of the lines between the Xbox and Windows 10. There's more stuff coming, too, that Orullian can't talk about just yet. But for now, the Xbox One is laying the groundwork.

"Everything will be unified at some point," Orullian says. "This is a really big, important part of that.