That makes me so happy! When we set out to make the inner game, we wanted to go for a Doom sort of feeling, so to hear that it felt like Quake makes me feel like we did a good job emulating that feeling.
I am really proud of my whole dev team, our artists and musician totally nailed it imo.
Just so you know, dying in the inner game does not actually mean it is a game over, it just reduces your final score at the end so you can still finish the game and get a presentation grade. But you will need to not die or miss any questions to get that juicy "S" rank ;)