I'm a bit hesitant to buying some video games through the google app store because I don't want to only be able to play it on my phone. If I bought some of these retro games I have and play them through Google TV (chromecast)?
I have one last question. Would I be able to play these games through stadia? Thanks! I'm a big retro gamer. I am dying to play many games I grew up with.
Stadia games are only bought through Stadia app and not the Play Store. Must check capability of games by seeing if they are available in Play Store on Chromecast and then buy them on Chromecast or through PC to make sure you are getting the game that is GoogleTV/AndroidTV compatible.
Depends on the game, but mostly yes. Some games are tagged so they aren't able to be installed on AndroidTV/GoogleTV devices, while others may install but cannot be played without an actual touch device (e.g. Organ Trail).
You'll also need to make sure your input device works properly with the TV. I have a wired Xbox 360 controller that works with most everything, my phone included, but when I use it on my TV there's major input lag.
Sure, just download and apk of a game from internet and install it on google tv. Unless this possibility is blocked for google tv (because its possible to do so on android tv).
There's a difference from games on play store vs. games on play store for Android tv. For example, I bought Stardew Valley on android store and it's not available for Android tv. It goes from game to game. Better check each one on the internet first. Also check if the Chromecast will have enough disk space for games (Im out of the loop when it comes to chromecast so I don't know how much internal memory they have or if they have any kind of USB port)