Furthermore, either desktop is no longer relevant as the New Guard (Apple, Google) want us to believe, in which case Microsoft's past and current dominance on desktop is a fairly moot point as far as today's technology is concerned
OR desktop remains relevant and we should be pressuring the New Guard to prioritize innovation in that space.
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.