Their influence on desktop is slowly eroding, though, and the new battlefield is the internet.
I personally strongly prefer modern "desktop" computing (that is, working with a computer with large displays while at a desk; I don't care what form factor the actual box takes) to computing on small devices.
Separately, I tend to like Microsoft's products more than Apple's and Google's even though I'm not a .NET developer. I'm weird, I suppose.
But all that said, Apple and Google are right that desktop is not hot—even a fan of desktop computing like myself must admit it's fallen out of favor. I've had my share of rants about why that is and what could be done to address it if firms are interested. But putting that tangent aside, I find those who bemoan Microsoft's dominance on desktop are using the wrong angle. If you like desktop computing like I do, but you don't like Microsoft, don't attack Microsoft. Instead, ask your favored firm (Apple, Google, whatever) why they don't offer you something you'd like in the desktop space.
I for one never agreed with past depictions of Microsoft as a monopolist on the desktop even through my experiments with oddball alternatives like OS/2. Their tricky business being what it is, they were not a monopoly. There were other options, but I eventually realized that I didn't like the alternatives.
Finally, I'm not sure I precisely agree with the implied shift from "desktop" and "the Internet." I figure I understand what you mean, but I can't help but envision the popular Homer Simpson quote: "Wait, they have the Internet on computers now?" Being a desktop aficionado, my desktop computing environment is all about network-enabled consumption and creation.
I see the chief battlefronts as:
* Small-screen versus large-screen (where I favor large screen and want small screen devices to be subservient views on applications running on my application server).
* Federated or self-control with sharing via documented protocols versus the plain cloud (where I favor federated or self-control because I feel the plain cloud we have today has brought us tremendous lock-in and multi-device/multi-cloud chaos).
All of these involve "the Internet," being the common communication medium.
IMHO, it's not an issue of "desktop" vs. small device, but integrated applications and presence that works smoothly across platforms vs. monolithic and siloed apps that keep you on one device.
Nobody does this well yet, but the holy grail of computing is to be able to move from desktop to tablet to laptop to phone and have your apps, data, and presence seamlessly follow you around.
Mobile has lept ahead in perceived value because it provides an illusion of that integration. Since you have the device with you always, you get a taste of what having everything everywhere would be like. However, that is fleeting and the providers have jumped at the chance to make it a walled garden that feels open (since the device is always with you), but doesn't share or play with others.
Eventually, people will become aware that mobile only is closed and bad, and integrated open multiplatform will rise, whether that is based on multi cloud or personal cloud or whatever technology best supports that seamless transition between devices.
It's at least partially on Microsoft to come up with good reasons for normal people to use their platform over all other options, and they've fallen very flat on that note in the past 15 or so years - particularly in the consumer space. It'd be interesting to see a revitalized Microsoft really attacking this space, but the promotion of Nadella makes me think that this isn't really what the MS board has in mind.