The Turok series, 1, 2 and 3 were amazing games. Even though the 3rd one was a downgrade as they attempted to make it a openish world were some of the best games of there era in my opinion. I loved the universe. The trilogy needs a remake.
While I agree with most of your points I mist point out you have it backwards the first 2 games featured semi open world design while the 3rd game adopted linear level design in a attempted to be more like half-life.