Oof good question! Like you said before I actually do have a list like that I’ve made before. Most games were Zelda, Mario, Kirby, Pok?mon, Harvest Moon and Sonic games just because I tend to like RPG’s over online multiplayer games. I like how intricate the stories are and prefer that over good graphics or online gameplay. I don’t think I’ve ever really played a Disney game except for the first kingdom hearts! Honestly the only newest games I’m playing right now are Pok?mon: Ultra Moon and Pok?mon: Super Mystery Dungeon.
As far as storylines go I’m a huge game of thrones fan, that’s definitely my favorite series right now. I’m also really into vampire movies (blade series, underworld series, van helsing) and the dark knight series too. Also the Castlevania anime series on Netflix. I’d love to find games with that darker feel!
I understand! I like RPG and solo games more than online, too. The only online I really enjoy is some fighting games, and then only a few. What's good about fighting games is that they're all very unique and each have a different gameplay, so I pretty much found the style that I like and just go with it.

This generation of gaming is blessed with an incredible amount of story-heavy games, so you're in luck! :3
Oh, if you liked the first Kingdom Hearts, then definitely get the
"Kingdom Hearts Story So Far" collection +
KH 3 on PS4. They're all brilliant and will definitely keep you occupied for a long time. :3 Story So Far has 9 games! Kingdom Hearts 1 was the first one in the series, and they started expanding the main story-line of the series with every game, so there's quite a bit to it now, and it's not just about Disney.
If you like Pokemon Mystery Dungeon, you'd probably be interested in
Chocobo's Mystery Dungeon on Switch! It's a pretty sweet game, not really story-heavy or anything like that, but if you like Pokemon - this one should be to your liking!!
Game of Thrones? Nice! ^_^ There's actually a game based on the show and it's called "
Game of Thrones Telltale", it's kind of like a point-click adventure type of game but with heavy focus on story and dialogue choices. It's not as good as the show, but pretty interesting! And some characters like Tyrion, Cercey and a few others are actually in the game and they're voiced by their actors from the show.

The game has its own story-line and it's not really "canon", but I'd say that what happened in the game makes sense and it could definitely be seen as "canon".
As far as "similar to GOT, but not GOT" - have you thought about Dark Souls? It's more focused on gameplay than story (though, it does have a story) but if there's a game that I'd ever recommend to a fan of GOT, it'd be
Dark Souls series. There is three of them and they're all good but Dark Souls 1 and Dark Souls 3 are the ones I recommend to play first, they're the best of the series and the 2nd game is fine but it was made without its creator, Hidetaka Miyazaki, so it's a little unrefined to say the least. And there's actually a collaboration game between Hidetaka Miyazaki and George R.R. Martin called "
Elden Ring". It doesn't have a release date yet, but I'm pretty sure you'd like that a lot. And there's also
Bloodborne game which is very close to the vampire feel that you mentioned!! Made by Miyazaki, as well. :3
Vampire... hmmm, let me think.
Ah! There's
Code Vein game coming out in September and it's going to have some vampire themes to it. Basically, vampires + anime style + Dark Souls gameplay. Definitely should interest you, I'm excited for it, too! <3 One thing to know is that Dark Souls, Bloodborne and Code Vein are quite difficult, but you can always find someone to help you in co-op. The game is gameplay-heavy but there's a lot of "contextual story-telling" which means that the games tell their stories with the items you acquire, with the places you visit and little bits of info that you see. Though, Code Vein is going to be more standard story-telling, so if you don't really like the idea of contextual, then Code Vein should be a safer bet!
And last one - I've noticed you mentioned Blade films. While not exactly the same, there's
The Evil Within series which is kind of similar to Blade. The 2nd Evil Within has this moment where it felt very much like one of the Blade films!
The Evil Within 2 is the one I'd recommend you to start with because it has a more personal story and you really don't need to know what happened in the previous game to start it. It mostly deals with the themes of grief, acceptance and guilt. The first Evil Within is quite good, too but not as good story-wise - interesting, but not as personal.
Here! I've recommend you a ton!! xD Let me know if you like any of these games. ^_^ And I've added a trailer for The Evil Within 2 in the spoiler.