Actually, they used their quasi-monopoly on search to push their browser. Anytime you visit Google with a non-Chrome browser it tries to push Chrome on you.
Funny you mentioned that... because every time I fire up Chrome in Windows 10 it gives me some Ad pop-up saying how much faster Edge is than Chrome or how much safer it is. I think things are getting pretty bad for the Edge browser stats... if they have to get the OS folks push their browser.
It is masked but always present. I don't know who built to it. It came before the first kernel.