TextEdit has has an integrated auto-installer that worked fine back in the day, but runs afoul of permissions in modern Windows versions. For the auto-installer to work, run TextEdit.exe as administrator. (You only need to do that the first time; it's not necessary for regular use.)
If you run the executable directly off this web site, you might also run afoul of Windows' protectivity. Download the file, right-click and select "Run as administrator".