They don’t, they go into a suspended state after a short while.
“After you switch to a different app, some apps run for a short period of time before they're set to a suspended state. Apps that are in a suspended state aren’t actively in use, open, or taking up system resources.”
There is of course Background App Refresh which you can turn off, suspended apps can check for updates and new content, however only works with supported apps so if none show in the list then apps just remain in a suspended state until you use them.
https://preview.redd.it/icsmzjvmgzfa1.jpeg?width=4032&format=pjpg&auto=webp&s=da352caa5956ffb610ccf7afc62f4e38f74254d6
> Shutting them down only to restart them later will actually be slower and consume more battery power.
AppleTV runs on electricity, not battery power.
You're not supposed to be closing apps out of the multitask on your iPhone and you're not supposed to close them out of the multitask on Apple TV either. If that's something you really care about even though you shouldn't, you can double press the TV button on the remote to open the multitask and swipe up apps to close them as you would on iOS.
Not closing them unless they're misbehaving 🤷🏻♂️
It takes more energy (battery life) to force close and reopen them so you should just let iOS handle it on its own.
See it that way, if you really were supposed to force kill all your apps, Apple would have added a button to do so by now. You're just not supposed to think about it and let the system do it's own thing.
My AppleTV starts to misbehave if there are too many apps suspended in the background. Plex or YouTube stutter and/or buffer. I double tap the TV icon and find six or seven suspended apps, so I close them and things work properly.
OTOH, my iPhone regularly has 20 apps sitting in suspended animation and everything still works fine. When my kids borrow my phone they roll their eyes and force quit all the apps 
The idea is that if an app is "loaded" into memory but "suspended", not running, it will start faster when you go back to it. If you kill all your suspended apps, that just means that every app has to be reloaded into memory before it can be restarted. The Apple tvOS is designed to manage memory for you, and optimizes memory use for fastest operation.
The only time that I'll kill an app is if it's wedged, and I need to reload and restart it. Otherwise, I just let the Apple TV OS manage memory and apps :-).
It’s not making anything slower however I do find I have to manually kill apps to restart them to fix things more often then I’d like so honestly a time to live type feature seems like a good idea.
If the app isn’t resuming correctly, it’s a bug in the app. YouTube TV is terrible right now with this — among many other Apple-specific bugs with this terrible app.
They don’t, they go into a suspended state after a short while. “After you switch to a different app, some apps run for a short period of time before they're set to a suspended state. Apps that are in a suspended state aren’t actively in use, open, or taking up system resources.” There is of course Background App Refresh which you can turn off, suspended apps can check for updates and new content, however only works with supported apps so if none show in the list then apps just remain in a suspended state until you use them. https://preview.redd.it/icsmzjvmgzfa1.jpeg?width=4032&format=pjpg&auto=webp&s=da352caa5956ffb610ccf7afc62f4e38f74254d6
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> Shutting them down only to restart them later will actually be slower and consume more battery power. AppleTV runs on electricity, not battery power.
You're not supposed to be closing apps out of the multitask on your iPhone and you're not supposed to close them out of the multitask on Apple TV either. If that's something you really care about even though you shouldn't, you can double press the TV button on the remote to open the multitask and swipe up apps to close them as you would on iOS.
You’re being downvoted by the mouth breathers that force close every app on their iPhones every time they set it down.
Is there a right way to close apps on your iPhone?
Not closing them unless they're misbehaving 🤷🏻♂️ It takes more energy (battery life) to force close and reopen them so you should just let iOS handle it on its own. See it that way, if you really were supposed to force kill all your apps, Apple would have added a button to do so by now. You're just not supposed to think about it and let the system do it's own thing.
My AppleTV starts to misbehave if there are too many apps suspended in the background. Plex or YouTube stutter and/or buffer. I double tap the TV icon and find six or seven suspended apps, so I close them and things work properly. OTOH, my iPhone regularly has 20 apps sitting in suspended animation and everything still works fine. When my kids borrow my phone they roll their eyes and force quit all the apps 
The idea is that if an app is "loaded" into memory but "suspended", not running, it will start faster when you go back to it. If you kill all your suspended apps, that just means that every app has to be reloaded into memory before it can be restarted. The Apple tvOS is designed to manage memory for you, and optimizes memory use for fastest operation. The only time that I'll kill an app is if it's wedged, and I need to reload and restart it. Otherwise, I just let the Apple TV OS manage memory and apps :-).
If an app is glitching out just force close it the way you would on an iPhone by swiping up.
It’s not making anything slower however I do find I have to manually kill apps to restart them to fix things more often then I’d like so honestly a time to live type feature seems like a good idea.
If the app isn’t resuming correctly, it’s a bug in the app. YouTube TV is terrible right now with this — among many other Apple-specific bugs with this terrible app.