I finally got this to work, but it wasn't easy. First, note that my "Windows tablet" is a fully functional 2-in-1 (removable keyboard) computer running Windows 10, both traditional desktop applications and tile-based Windows Store apps. Since the new Edge browser does not support extensions (yet), I use Internet Explorer (IE) 11 in its desktop application (not tiled) version.
When I tried to use dishanywhere.com with IE11, it downloaded and installed a WBsomething.EXE file, but that never made DishAnywhere work, so I uninstalled it. I searched the Internet high and low--there were no other download options offered to IE11.
Then I downloaded and installed Google Chrome. When I opened dishanywhere.com from Chrome, it downloaded and installed a DishAnywheresomething.EXE file. That put a shortcut on my desktop named "DishAnywhere SlingPlayer" (yes, both words are in the name), and when I started it, it put its icon in my system tray. With that loaded, Chrome could fully use DishAnywhere.
So now, with the new DishAnywhere SlingPlayer icon in my system tray, I launched IE11 and returned to dishanywhere.com, and this time it worked perfectly. With this working, I could uninstall Google Chrome, and IE11 continued to work fine.
Since I'm only slinging the Dish content on my home network, not up to the Internet, performance is very good. As the previous poster noted, there is a delay when I use the FF or Back on-screem "buttons", so I have to be careful not to press either too many times.
This is a great solution, but only if Dish will drop that WBsomething.EXE download, and offer IE11 the DishAnywheresomething.EXE download instead, without having to involve Google Chrome. And for goodness sake, clear up the confusion in the DishAnywhere vs. SlingPlayer names!
My thanks to everyone who tried to guide me in this thread.