Not whole game, most of the part.

What's the genre?

Action / adventure / hack & slash

Shadows of Mordor? I remember hearing that one has some kind of a revenge plot against the orcs or something, and your character is on a murdering/killing rampage throughout the game basically.

Yes, it's Middle-earth: Shadow of Mordor (2014) by Monolith Productions. Surprisingly decent game.

Hence your turn

Ah, I read a review that said the opposite.

Teenagent!

Don't read reviews. Play games or watch YouTube at least. Metacritic score is high enough even. Of course this isn't a gem in gaming industry, it can be boring at times, though battle mechanics is fun-fun-fun. Forget about plot, there isn't one. I also laughed about cut scenes and additional plot elements because they are meaningless. Gameplay on the other hand is enjoyable.
What??? Are we playing already? ;)

Ahaha, a good one! :)

To be honest, I'm not really interested in games like Shadows of Mordor because I usually play games for their plot and dialogue, so most pure action games aren't much fun for me unless they have a really good combat system like Dark Souls, because mashing few repetitive combos to kill horders of incoming enemies like in most games (or clicking) isn't doing it for me.

Here's the actual new game. ;)

Once I battled a legendary vampire. Now I'm just wading through scores of goblins, orcs and other creatures.

Hmmm, reminds me of Arantir's campaign in HoMM5:TotE. :-)

On a more serious note, can you describe the protagonist? What does s/he look like, what does s/he wear... is s/he even human?

Castlevania: Curse of Darkness ?

http://castlevania.wikia.com/wiki/Orc

No, but that is/was one of my favourite games. Not sure if this one actually had orcs though, I don't remember meeting any in this game.
Yes, the protagonsit is human, he wears a black hat, a red scarf and a black coat, however you can change his appearance depending on what you make him wear.

Probably one of the Van Helsing games then. I know of two, but I've played neither so...
Is it The Incredible Adventures of Van Helsing?

Yep, you're right! I plan on playing the game eventually (or the second one, not sure which one is better), once I buy it. Preferably with some friends. :)

Both games were part of a HB bundle some time ago, and on a PWYW tier to boot. Might eventually resurface there.

You start the game as a prisoner in a cell, listening to your neighbour from the next cell mocking you and describing how you'll die here. No emperor comes around to save you, but instead a sizeable rock hits the wall, killing your neighbour and giving you a chance to escape... problem is, you have no weapons, no armor, no money, no nothing. Well, time to go look for some of those things... you might even find some companions with useful skills, who knows?