According to Hoffman, when he tried to install Firefox on a Windows 10 Insider build, the installer was temporarily blocked and a Window was displayed stating "You already have Microsoft Edge - the safer, faster browser for Windows 10". They were offered two options: "Open Microsoft Edge", and "Install Anyway".
Whether or not such prompts would tag along with future Windows updates, would depend on the feedback on this particular test feature. It's particularly bold for Microsoft to surface this pop-up as soon as you try to launch the installer for another browser as well, and we can't really see its existence sitting well with the larger Windows 10 userbase. Judging from the current implementation it will be opt-out which means that the intercepting prompts are displayed to all users by default who attempt third-party software installations.
For example, when visiting Google.com using Edge, you will see dialog boxes that make statements like "Switch to Chrome". Now it's being used to trumpet Edge, too.
Microsoft has released Edge for Android and the browser has been well received by Android users. However, Microsoft hasn't been successful in doing so and the market share numbers are the proof of that.
Prompts of that sort can be turned off by using the link under the buttons on the popup. It shows a smiling person standing in front of the Edge logo, leading what is presumably their best life now that they've broken free of Chrome and Firefox. Microsoft trying to tempt people back to Edge through alerts like this isn't really anything new, but this time, the pop-up shows when you open the installer for another browser.
WTF?! As demonstrated by the methods it used to get people onto Windows 10, Microsoft isn't averse to using shady tactics when pushing its products.