[kevingadd]

Yes and no, for example Morrowind on the Xbox used a trick where it would silently reboot your console at loading screens to free up memory, and the console would boot directly into the game. https://kotaku.com/morrowind-completely-rebooted-your-xbox-d...

You could certainly still say that the 'game ran under the OS' in this case since the kernel and drivers were underneath it, but I think it's fair to consider that a different beast from more modern consoles that have a full OS available underneath that you can summon with the home button and does things in the background like maintain a persistent network connection, do background downloads, etc.