Is there a question? I think this text is way better than a lot of games I've played. Don't worry about it.

Looks great to me, but then again, english isn't my first language either. Since it's fantasy, you can turn this into an advantage, as the dialogue may sound faintly foreign, different from the player's everyday speech.

The text seems fine to me too. There are some minor typos and maybe one or two things might be said a little bit differently by a native English speaker, but it makes me want to get to know the character and play the game, which is probably a good thing :)

Dirt in not human...

Usually the phrase "is not human" would have a negative meaning, but you are trying to be positive about dirt here. So instead I would say "Unlike humans." or "Not like people. People are never trustworthy..."

I miss my old life. I miss being a farmer. Sometimes I wake up late at night, cold and sweaty, and my hand itches. It itches to hold a plough once again. Just once more. When that happens, I have to clench my fist, usually over my ax's handle. The ax is so cold, it removes all though of dirt from my mind. The ax doesn't like dirt. Dirt hurts the ax. The ax only wants one thing: the ax wants blood.

Aside from the thought/though typo, I question the logic here. An axe handle is very similar to a plough handle. Blood enriches dirt. If dirt represents the opposite of people, blood should be thematically allied with dirt because blood represents the removal of people.

Once I pick up that ax - there's only one thing to do - I need to fulfill its demands.

I personally would use a comma instead of the first dash here. Not very important though.