The game is treated as a series reboot and bears no relation to the continuity of the previous Turok editions or to the comic books.
The player takes on the role of a soldier named Corporal Joseph Turok. Previously, Turok was a member of the Wolf Pack, a specialized military detachment whose members were trained in black ops by General Roland Kane. After a falling out with the group, Turok was reassigned to a general military unit known as Whiskey Company. The team has been assembled to apprehend his former mentor and return him to Earth. After committing various war crimes, Kane had disappeared three years earlier only to surface on a backwater world. Unbeknownst to Whiskey Company, the planet is under the jurisdiction of the Mendel-Gruman (M-G) Corporation, and Kane is in command of a private army of M-G soldiers and equipment.
At first, the crew shuns Turok, thinking that he is an inexperienced fighter, untrustworthy, and a liability. One particular member, Slade, has a personal grudge against Turok because his brother Robert was also a member of Wolf Pack, and was killed in the same battle in Columbia from which Turok had reputedly fled, earning him his dubious reputation.
On approach to their destination, their starship is shot down from orbit and crash lands on the terraformed surface, where Turok quickly learns that the jungles covering the surface are inhabited by genetically engineered dinosaurs. The dinosaurs are wild and dangerous, and are also being used as experimental weapons for General Kane, meaning a three-way battle between Whiskey Company, the M-G soldiers, and the dinosaurs takes place throughout the game.
Source: Wikipedia, "Turok (2008 video game)," available under the CC-BY-SA License.