Unfortunately no. The sling adapter is a lesser version of a Slingbox. It works with Dishanywhere and is for watching Dish only. A slingbox can be for any source of any provider, some even can get OTA and have a built in tuner, or for security cameras and a lot more. The app in a WD Live player will work only with a slingbox.
That said, you can hook your computer to your TV and get a bigger picture that way. Prior to the APP being in the WD player that's what I would do if more than myself wanted to watch. There are other ways to get the picture to the TV. If you have a Roku it will take the picture and sound from a mobile device that has the Sling app (again for slingbox only) and put it on the TV. Some TV's now will take whatever you are watching on a mobile device and show it.
And with a little experimenting, the $35 Chromecaster will get it to the TV from your computer if you use the Chrome browser and that may work when you are watching from Dishanywhere.