The Texas Department of Public Safety identified the man as 23-year-old Esteban J. Smith of the Camp Lejeune Marine Corps Base.
In a statement Monday, Department of Public Safety spokesman Tom Vinger says Smith later died in a gunfight with an agency trooper and a state game warden.
Six others were shot, one fatally, in the roaming rampage across the rolling plains of West Texas on Sunday.
Three people were treated for their wounds in hospitals and discharged. Two others, including Concho County Sheriff Richard Doane, remained hospitalized with non-life-threatening wounds.
Camp Lejeune officials did not immediately respond to requests for comment Monday.