Yep! The pilgrimage gave it away, right? :)

Yes indeed ;)

Let's start: My dear king Ragnar was attacked by local wizard Guthbert which in turn named me a culprit. That is why I absolutely had to run away with a few servants for... hunting in the farthest borders of my kingdom. We found a narrow passage there with a portal and somehow managed to place an invisible barrier behind us, so no one can find us. A new uncharted land appeared in front of our eyes, the sun shined differently, the air was more humid, even the gravity felt stronger here.
I don't have any other choice but to conquer new land under my banner. I'm a rightful ruler!

I'm not sure but i think this could be Heroes of Might & Magic. One of the old ones.

Indeed, it's Heroes of Might & Magic One

Okay. Let's see:
After i tried to destroy the ship of my former commander i crashlanded on a planet whose population has mutated into feral tribes. Trying to satisfy my thirst for revenge and getting of the planet i have to fight them. A powerful tool found in an escape pod might be useful.

No one? Okay: Additional hint: it's a fps

Halo?

No. It's a more mature game in terms of dialogue and violence...

I'd say Albion but you didn't try to kill your commander and they aren't feral tribes.

Can you say something about why you try to kill him?

Because he duped me and my team earlier. He made us kill innocent people...

Gunman Chronicles?

No. Another hint:
- Just to clarify. The ship from the former commander also crashed on the planet...
- and i team up with a child of one of these innocent people my team killed

Bulletstorm?!!

Yup. Your turn.