Narrative can totally affect the feeling of a game, the structure more or less depends on its storytelling, if it isn't an overarching narrative then it's environmental storytelling, but they usually go hand in hand, so if the story is for instance flat out annoying it can make the gameplay annoying also, in the case of Doom Eternal the gameplay is strong enough to hold its own (the combat at least) but the story has a huge emphasis on why you're there and what you're doing at any given time and the cutscenes constantly support it so I find some parts of the game to be not that fun or just kinda boring. If the story was really good then I would be constantly immersed and it would actually make the gameplay a little better, or even allow the gameplay to be serviceable at best if the world building is great.