Ghostbusters: The Video Game/WMG

"Rookie" is the rookie's actual surname.
As a shout-out to Kill Bill, the new Ghostbuster hired in '91 has "Rookie" on his name tape because it's actually his name, not because the Ghostbusters just have a standard-issue "new-guy" jump-suit they make new hires wear out of black humor for their employment duration expectancy (or, for that matter, their life expectancy.)
 * And "Scooter" is his first name.
 * Alternately, his last name is Rook, and Rookie is just an affectation.

The mechanics of a Destructor form, as a happy side-effect, actively neutralize the negative effects of Crossing The Streams.
And Egon's figured it out, too,
 * I figured it just destroyed the dimension they were in. Since both times, they were in a projected "pocket" dimension invading ours; it canceled that out. It just turns out that humans, when subjected to No Space, return to their point of origin; ie Earth.
 * Definitely better than the basic idea's handwave nature; let's add that powerful non-humans don't have much trouble with dimension-crossing, otherwise it would beg the question of how Gozer still exists after the first movie. Backed up by Ray's polite request specifying that Gozer could return either to its place of origin or "the nearest convenient parallel dimension."
 * Oh, that's easy. Stay Puft was a Projected Avatar. (it actually says this in the scan data in the game). Only part of it is in our reality. The first movie, they don't actually beat it directly, they cancel/reverse the gate connecting the Stay-Puft Avatar to the Gozer existence outside our reality. In the game, when they (or rather, The Rookie) kills it, this sends it back to the Outer Darkness Dungeons and Dragons style.
 * Isn't that more or less outright stated in the film? They couldn't "kill" Stay-Puft; shooting him just made him angry and on fire. Crossing The Streams into the portal reversed the spectral energy flow into our world and closed it off.

Ivo Shandor's family are descended from Tiamat worshippers.
According to the Gozer exhibit at the museum in the Realistic-Style version of game, Gozer was a major power on Earth before Tiamat and her followers (Not the Dungeons and Dragons one, the Babylonian one) defeated it and banished it from our reality. Interestingly enough, one of the collectible items in the Realistic is a painting of the Shandor Family....on "Tiamat Island." Being descendant of the ones who banished Gozer gave him the knowledge of how to reverse the effect when he turned to the Dark.

Walter Peck really is a Gozer worshipper
Remember he had a high PKE level in the Museum, even after he was slimed to remove possessors. The reason
 * In alternative, Walter Peck was so dumb he never figured out that, and his high PKE level was only due to the fact that he was an ass-kisser. Literally.

Before getting hired by the Ghostbusters, the rookie was...
Assuming there's not some Word of God I missed;
 * A college student, maybe still is, and it would fit with the main four's Badass Bookworm status.
 * In the military; he has little trouble learning how to use a projectile weapon, doesn't flinch at wearing the hundred-pound metal ruck said weapon is attached to, adapts quickly without panicking over extraordinary things, is good at doing what he's told, and considering the friendly AI, could believably have combat training going for him compared to the scientists.
 * Nobody special; a fan who applied with a "hey, why not?" mentality never expecting to get the job, and only got it because anyone more qualified ran away screaming after meeting Slimer up close for the first time. This would be some benign Reality Subtext, since the Rookie is modeled after the game's associate producer and Ghostbusters fan Ryan French.
 * An extremely minor or extremely subtle deity, or at least a human with some divine blood in his veins, possibly a descendant of Tiamat. Let's be honest here, if he hadn't been around; the Ghostbusters would not have had a chance against the deities they fight in the game. The whole Heroic Mime routine and No Name Given thing is a side effect of a cloaking he uses so that other deities can't detect him. Notice how while the other 4 Ghostbusters can get possessed, he can't. Has also extended the power of healing to everyone, so that all it takes to recover from fireballs and massive blunt trauma that would disintegrated a normal human is to take a breather, or if knocked down; get touched by one of the others or wait a minute in the others presence if they're not knocked down too.
 * An ex-member of either the MIB or the BPRD.
 * OR! He's a young Meyers.

The Rookie is The Voiceless because...

 * A ghost stole his voice as a child. Now, he really can't speak, but he is a believer in the supernatural (because it happened to him), highly motivated to bust ghosts (to prevent anything like that from happening to anyone else), and by siding with the Ghostbusters, there is a small chance he can recover what he's lost. The senior team members, being former professors, have familiarity with sign language, and the Americans with Disabilities Act covers the rest. He can do his job with reasonable accomodations, after all.

Ivo could only maintain a Destructor Form in that pocket dimension in the end, the battlefield where he fights the Ghostbusters.
Although he had all the PK energy he required via, according to Ray he still needed a. But that never happened. Had he won, he would have been able to still fulfill the ritual, but what they fought wasn't a true Destructor who could walk the earth.
 * This is supported by Shandor's constant recharging during the final battle of the game. He was only capable of taking the Destructor form due to the massive amount of spectral energy he absorbed from the Containment Unit's ghosts and, potentially, Gozer itself.

Each depiction of the Rookie will start a new Franchise in one of the three cities.
What "really happened" is a mixture of both the Realistic and Stylistic plots. So they actually had 3 Rookies. The Realistic Guy, and the Stylistic Guy, and the Stylistic Girl. Each one will set up a different franchise in Chicago, Los Angeles, and Cincinnati.

The "Rookie" name tag was just a placeholder until the rookie could get the custom-ordered tag that bore his actual name.
Presumably, the other Ghostbusters wouldn't have referred to him by name until the custom tag arrived, and the tag didn't arrive until they had defeated Ivo Shandor's plan.

The previous rookie suffered A Fate Worse Than Death
Peter says he doesn't want to get too attached to the current rookie because he remembers what happened to the last guy. We don't get to know any more than that, but one of the bonus contents, coming from a Best Buy download code, is a new player model: a ghostbuster with no skin on his head as well as no lower jaw and missing part of his neck muscles, whose name tag reads "Scance" and is referred to as a "ghoul". This troper thinks that Scance is the previous rookie, who was turned into a ghoul in an accident during his final mission, before the events of the game. His ability to follow orders and catch ghost when used as a player character shows that his mind was not affected by the changes in his body and he is still lucid. Thus, we may also imply, he remembers his life before becoming a ghoul and wishes he had just died.

The 2009 Ghostbusters video game IS the "CGI" Ghostbusters 3 that was originally announced
Supported by the fact that the game had not been officially announced when the first reports that the third installment would be CGI rather than live-action were made - the game WAS CGI, like any 3D game, complete with CG versions of the original team. Also by the fact that the game is a very direct sequel to the first two movies, and ties in heavily with the plots of both, tying up numerous loose ends and elaborating on the weirder plot details of the films. While there may possibly be a third film in production (I don't remember where I heard this, but I do remember hearing it from somewher; whether it was reputable info or not I'm not at all sure), I think that the announcement that 3 would be all-CGI was just a clever way of announcing the third installment and giving a small bit of truthful info without outright revealing yet that it would be a video game.

Walter Peck is a Sin-Eater
This could explain why he had such a high PKE level in the video game after he was no longer possessed. He died in the first movie after being buried under marshmallow and was brought back. The PKE meter was able to detect his Geist even after it had fused with him.

The game was once supposed to be set in the present, not in 1991.

 * Evidence #1: the conspicuous lack of Twin Towers.
 * Evidence #2: Peter says: "Times Square, post urban renewal." But the renewal took place in 1993.
 * Evidence #3: an early version of the game has a cutscene where the Rookie's name tag reads something that ends in -ETT. As in "Barrett". As in Oscar Barrett, born in 1989, who could only be an adult if the game was set in our present time when that cutscene was made.