Sure, but I will never understand why somebody would buy a fighting game for the story. Well, I guess I could with Persona, because fans would probably care for it coming from an RPG, but otherwise...I don't get it. Never have, never will. Just completely foreign to me. Stories in fighters are invariably garbage and if you care about stories, you'd be better of playing games that put more effort into that aspect.
I can't speak for the genre in general, but I for one have been following SNK's stuff for years, and throughout those decades a lot of lore and subplots build up in different but connected games, some of them left hanging for upcoming games - individually each doesn't amount to much, but paying enough attention to each and how they follow from each other it ends up being like following a favorite TV show, only each episode takes years to come out.
As an example, I'm still kinda of hoping someday SNKP will bother to release a game that shows the results of the training depicted in my avatar here, for example, since that's got quite a bit going behind it, and at the same thing it would imply some merging of fighting styles from 2 or 3 characters which I'd be curious to see in action. Garou 2 would do nicely.
Having first become aware of some of the stories at an earlier age may have applied something of an imprinting effect to the whole thing, so grain of salt and all that.
For DoA I can't care as much, because in the end it always seems to boil down to ninjas running around and stuff exploding, but I did watch some videos of Dimensions, and that seemed to tie more closely into the Ninja Gaiden series (at least I think one of the NPCs with Hayabusa was from that), which was nice - at least I like it when stories are included in the context of a larger world.
For 5, I didn't expect much, though the trailers left me curious about a scene or two (Hitomi and Leifang going all Jungle Jane WTF?...), but there were still some nice moments, like the Bass/Tina meeting in the tournament, which for the genre wasn't a terrible handling of a father's concern for how his daughter is handling her life and how she deals with his attitude about it.
I wish the VF characters appeared more than once, and that Pai made her way in there somewhere, it would have been hard to replace Mila with her in Leifang's story mode.
Barely related, but am I the only one that finds it weird that you get no titles in DoA5 for finishing Zack's chapters in story mode like everyone else (well, Kasumi gets 3)? He's degenerated into a joke character years ago, but still, he's got a bit of a role in the events...
Also barely related: does akira ever actually say "Jyunen hayaindayo!" in the game like he did in the reveal trailer? He always says something else in his intro and victory animations... It's weirder still that he doesn't ssay it when challenging Kokoro in her story mode, but Zack jokes about that line (something like "those 10 years went by pretty fast") when the fight's over.