Or conversely, how do you use an rca universal remote to change video input for the dvd/vcr player?

It is difficult to say for certain if a button labeled "Game" changes the input on the TV or not. Press it and find out. Some "game" buttons will just change the picture settings of the TV. Others might switch to the front connection of the TV.

Using a universal remote to change inputs depends on the remote itself. Even beyond the brand. RCA makes several different universal remotes. But once it is programmed for the TV, try pressing a button labeled "source" or "input". If these buttons don't do anything, try another code. It is likely with an Emerson TV that you will not find the proper codes to make everything function perfectly on a universal remote.