This game takes place in 1990, one year before the 2009 game.
Immediately following the Vigo incident, business dried up yet again. After a few days of no calls, Winston left the fold and went back to school full-time, eventually getting his doctorate sometime in mid-1991. Since he mentioned Egyptology, it's possible that he was in Egypt during the events of this game, and could not be reached when things picked up again. The "Weapons Shop" dealer built prototype Ghostbuster tech when he and Arthur were friends
Aware that Arthur's proclivities could easily spiral out of control, the Weapons Shop guy built equipment that could potentially counteract whatever Arthur might bring into our world. The stuff probably didn't work very well at the time; it was only when hooked up to the Proton Pack that the various gadgets truly came into their own. The theatrical ending of Little Shop of Horrors is canon within Ghostbusters lore via this game
Seymour (played by Rick Moranis) annihilates Audrey II, whose animus is drawn to the Castle, which serves as Arthur's base of operations. It drew corporeal inspiration from the ivy and moss growing throughout the castle, eventually growing even more powerful upon eating the "Eye of the Flame" jewel.