I just purchased two "smart TV's". Both are Sony units. One has the Sling TV app and one does not. My wife says Sling TV will cover all her needs, so she subscribed to it. Now, she would like to access Sling from the Sony TV which does not list it in the apps section. The TV is the 43 inch model 720; and, my question is how can I add Sling TV to this set, without having to buy a media player like Apple TV or other? Of course, if my wife and I were more knowledgeable about Sling TV before purchasing the sets we may have chosen another set instead of the 720; but, that was not the case.
I have been a Sling TV user for quite some time. It works. It has its challenges, but it works.
Most devices that can support apps can simply add the app. I have the the Sling TV app added to my phones and tablets etc. We bought a "smart TV" that could add apps and we simply added Sling via the menu on the TV that let you search out new apps. That will be the limitation on your other TV : can you search out and add new apps? If it allows it, then you have a shot at simply adding the app via the menus on the TV.
If you can't, and there are plenty of "smart TVs" that are dumb as a brick and won't let you add an app, then you need an external box/device/computer that can access the app and pass the signal to the TV.
We at our place cut the cable cord years ago. We installed on over the air digital antennae and a DVR box from Channel Master that lets us do the TIVO style recording and scheduling for over the air TV. The Channel Master box will also add Sling TV as a channel. We simply go to our Sling TV channel on the Channel Master DVR and voila, the world of streaming TV is there.
You could also add Sling TV to a laptop and then just pump the HDMI out to the TV. And of course, all the media players will do it too.
Hope this helps.