Welcome to Android Central! What do you mean by downloading games from Google Play on your computer to the phone? Are you on the Google Play Store website, and trying to remotely install the game from there? On the game's Play Store page, click on the Install button, and then select your phone to install to. If you don't see it there, then the game isn't compatible with the phone.
Are you unable to find those games using the Google Play Store app on the phone?