It's all part of the same great blob of peripherals, to me. Just like "graphics" can be easy to dismiss in importance, as long as the core game is good, when in fact GOOD graphics stand only to make a good game better, I like it when a game that has great gameplay and graphics also has a great story. Not necessarily riveting, but enjoyable. Doom's story really was just an excuse to explain what that mess of a thing was ("mess" in the good, thrillingly hectic sense) and why you should care, assuming you needed a reason. It was simple, it wasn't great, but it worked, and its simplicity made it fairly air-tight to the ages. There wasn't much room to make lofty criticism of ludonarrative dissonance or schizophrenic plot beats or plot contradictions, because the story was just premise, and nothing else. The rest was the game you played. In some ways, it's the same with Portal and its story, though as with much of Valve's works, "story" was embedded throughout the game in Easter Egg type fashion, so that the game could have been played for its gameplay, or it could have been explored for user-driven exposition and optional storytelling. Demon's Souls and Dark Souls did the same, with the game being driven by story in a sense, but largely left to the devices of the player to enjoy at their leisure. If one were to pursue the lore behind the scenes, one would find a wealth of color to the world of your exploration, and I adored it for that.
In stark contrast, David Cage's work is often lambasted for fixating STRICTLY on story, and tangling it within a game that has ergonomically-challenged button layouts and mind-numbingly repetitive and inconsistent QTEs to make up the mainstay of a game that otherwise lacks traditional "gameplay" in any typical sense. Somewhere between these two extremes is where I enjoy games the most!
I like that Ninja Gaiden has a solid story. It's nothing special. It's not particularly amazing. The twist at the end isn't much of a revelation. The game stands on its gameplay, and the graphics were superb for the time in which each iteration was crafted. The story was just kinda "there", but it worked, and that's what I liked about it. It was better than Doom's, not quite as complex nor remotely mind-fucking as Portal's. But I can't say the same for its sequels. Each subsequent title just added more bullshit and contradictions to the story. The nits you could pick with NG2 or NGS2 rivals that of FO3's nitpicking potential, and that's saying a lot! Gameplay wise, the first sequel added improvements but, depending on taste, took out some things you'd like, as well. It's the sum total of things that's why I prefer the first game over its sequel. It's just "better" overall.
Similarly (and again, predictably, given it's Valve we're talking about) Dota2's story is there, but largely hidden unless you decide to go looking for it. Each playable hero has a backstory, and even NPCs (which you won't even notice, unless you pay close attention) have a tale behind the scenes! It's all there, and it can be found in a variety of ways. You can learn about the relationship between Kunkka and Leviathan based on their dialog when they encounter each other in the game, both as enemies and as allies. You can learn secrets about the Arsenal Magus, the Invoker, if you successfully trigger a rare line of dialog. You can learn things about Leshrac's past and his traumas by repeatedly clicking him and learning his insights. There's such an absurd abundance of rich story in Dota2, but you wouldn't know it from simply playing the game. The game is meant to stand on a firm foundation of superb gameplay and night-flawless balancing. But Valve went the extra mile and made sure not to overlook that little extra flare in the game's story.
I don't know of any games that I've played (much less enjoyed) that were on the level of "nothing but story, fuck all the rest" like what Heavy Rain and its spiritual successors/predecessors were criticized for. Although I WAS interested in picking up HR, and simply never got around to it on account of losing my job around the time it came out, and avoiding its purchase for the sake of having something to eat. But now that I've got steady income once more, I ponder about getting it, years later. (I've managed to keep myself unspoiled, all this time! XD) But I do wonder how it will feel, if I were to find all those criticisms of the game turn out quite true. If it feels truly boring or if some of the scenes just feel like a drag or if its focus on story was wasted. If I pick it up, I suppose time shall tell.
I find it appropriate when they say these things are "only icing", because it's true! If all you eat is icing, you'll make yourself sick. But if you savor a delicious cake, good icing will only enhance the experience! By all accounts, Bayonetta's gameplay should be no different than ANY other game: it should be the foundation of that cake, the deliciousness that you savor. If the gameplay wasn't fantastic, it would deserve little in the way of praise. But icing shouldn't just be dismissed as totally optional. It should make the experience better. According to Jim Sterling, its story is delightfully ridiculous, and so assured of itself that he's totally along for the ride. It accomplished immersion in its own way, for him, in a very convincing fashion, and it was through the world and the character of the game, not just the gameplay. According to Yahtzee, he was just too distracted by Bayonetta's impossible and horrifying proportions (which I don't see, quite frankly; she looks good to me) to notice anything other than the gameplay, and he couldn't decide if it was his experiences with Dark Souls having refined his abilities or if B2 was simply toned down in difficulty from the prequel because he scored so much more consistently better in the game than the previous. According to others- I forget who, exactly -it's a thrill of a ride and it's not about the story. Sounds good. Just sounds like a cake that goes easy on the icing. =)