If you don't touch the screen the device will enter standby unless the app you are running tells it to stay awake. Chrome is not one of those apps. The YouTube app will also let it sleep if nothing is playing.
You can tell it to stay awake for all apps for up to 30 minutes. Not sure why you would want to as it would kill your battery by staying awake when you are not using it.
You can also tell it to stay awake while charging in the developer settings.