Based on research of the Laser Tag Museum, Star Laser Force was believed to have opened April 16, 1985. This assumes that the Houston Magazine article was in error when giving an October, 1984 opening date, a fair guess considering they mixed up a few details when describing Photon and Star Laser Force and their game play.
That article is no longer the earliest reference I have, though.
This ad in The Rice Thresher, the student newspaper of Rice University, has the same low-budget style seen in early brochures. The publication date of December 7, 1984 suggests that indeed Star Laser Force was open not long after the business name was registered with the County (September 7, 1984; file #638264). On this basis I find October 1984 plausible, leaving it still the 3rd laser tag arena to open on the planet, just after Laser Zone in Chicago.