the answer from "silverstorm" is correct. To elaborate a bit, if you add a feature or API to the underlying OS, but there's no corresponding browser feature that makes use of it, to someone who spends most of their time in a browser the OS feature may as well not exist. Microsoft's main reason for investing in IE has generally been to try to add to the perceived value of Windows by making new Windows features accessible through the browser and thereby more relevant to web-centric PC usage. Examples are taskbar integration in Win7, live tile support in Win8, the emphasis on hardware acceleration in IE9+ (which was designed to try to make the underlying Windows graphics system more relevant to web browsing), smooth touch panning/zooming in IE10+ (by being early adopters of the Windows DComp/DManip APIs), better font rendering on high-DPI displays via DWrite etc.
Note that if other browsers themselves adopt new Windows APIs in competitive response, that actually still benefits Microsoft because ultimately they don't care about the browser for its own sake, they care about increasing Windows API and feature usage across all browsers. But in practice competing browsers tend to be late adopters of new Windows stuff (e.g., even now nothing but IE supports DComp/DManip and Chrome is just very recently getting around to improving its Windows high-DPI and text rendering support), hence Microsoft funds IE.
Note that if other browsers themselves adopt new Windows APIs in competitive response, that actually still benefits Microsoft because ultimately they don't care about the browser for its own sake, they care about increasing Windows API and feature usage across all browsers. But in practice competing browsers tend to be late adopters of new Windows stuff (e.g., even now nothing but IE supports DComp/DManip and Chrome is just very recently getting around to improving its Windows high-DPI and text rendering support), hence Microsoft funds IE.