Microsoft Edge is a Universal Windows App that should be updated through the store just like other UWP apps. That is at least what Microsoft made us believe when they released the browser. Unfortunately, Edge has never been updated like other apps and instead has tagged along with Windows 10 via Windows Updates.
The reason is simple: Edge is a part of EdgeHTML, the engine powering Microsoft's browser and any web view elements inside applications programmed for the Universal Windows Platform. Think of UWP apps as jars full of liquid, standing on a gigantic container (Windows 10) with the same liquid. Edge would be a jar with a pipe connected to the container. Replacing that jar would make the liquid leak, which in reality would represent be the system breaking.
Now, Microsoft is planning to update the UI and some other parts of the browser through the store, as reported by Thurrot, by splitting the application into two separate packages. This will allow EdgeHTML to remain intact while the UI around it can get updated whenever needed. This change has been revealed at Microsoft Ignite 2016 at about 13-minute mark, in the video below:
But what does this all mean to consumers? It means that a lot of security improvements, bug fixes, and feature updates for Edge will come at a much faster rate than they do now. Hopefully, that will help Edge move beyond its current 5% market share.