You are correct in your observation that Edge (a Windows 10 exclusive) is changing it's browser rendering engine to Chromium. Chromium is open sourced, which is not the same as saying it is Linux. It's well understood that Linux exists only because of it's disdain for anything proprietary, but, technically, saying Chromium is Linux is comparing apples to oranges.
Regardless of what you call it, Edge is failing big time just as was Internet Explorer back in it's earlier days. Mozilla came to the rescue back then in spite of Microsoft's embedding IE into the operating system and thus forcing everyone to have a copy. Firefox displaced IE as the leading browser, but that is no longer the case. Firefox is fighting for it's life now because Google's Chrome browser is embedded into their Chromebook operating system exactly the same way as was Microsoft's IE. The difference is that Chromebook is basically a web based computer with none of the functionality of the so called Windows as a service (Windows 10). From what I gather they don't even offer a hard drive. It's all done in the cloud. The bottom line is that the Chrome browser beats out IE, Edge, Firefox, and everybody else when it comes to its market share.
Microsoft died when Bill Gates retired. They have been playing catch-up ever since. I'll agree that they have made great inroads into the mobile device market, but all of Microsoft's hardware is inadequate competition for anything Apple or Google are promoting. Lately Microsoft has overtaken Apple as the world's largest (by dollar valuation) company, but it's not due to their browser and certainly not because of their Surface product line. While Gate's vision disappeared when he left the company, that doesn't mean Microsoft suddenly became stupid. The idea behind the phrase "Windows as a service" is to insert the Microsoft brand everywhere. The new browser internals from Microsoft is just one more sign that they are recognizing the value of open sourced software, which is what Chromium happens to be. The irony is that this open source browser from Microsoft will cost you the price of their operating system if you want to use it. Likewise, you can run any Linux coded software in Windows 10, if you were inclined to do such a thing. I had Ubuntu running in my beta versions for quite a while. But, again, in order to use this open sourced operating system inside Windows as a service, I had to pay the price. Well, in my case it was free. But non-beta testers are paying.
I do believe Microsoft sees some value in open sourced software and playing nice with Linux. I don't believe they will bother absorbing Linux into their company. They are thinking big, and not niche markets. And, finally, in my humble opinion Microsoft is missing the point. Edge has some really nice features you can't find elsewhere, but it is friggin' slow to respond and it defaults to Bing search engine. The combination is deadly. I used Edge for a long time because I was beta testing, but now I've got a Firefox clone installed so that I can do some real browsing. I did suggest that they dump Bing, but for some odd reason they never listened to me on that count.
