Actually... in the original ADB design concepts for the game, there were no different types of phasers at all, just a Phaser. ADB designed the game based primarily on Franz Joseph Designs Star Trek Starfleet Technical Manual, and script writers documentation from the Original series. In those notes, a Klingon Battlecruiser was described as bristling with phasers all over it, like a Battleship. From a gaming point of view, if this were true, then Kirk should have had his a** handed to him nearly every time when fighting a Klingon D7.
So, to resolve this anomaly, and remain true to the material, ADB came up with the idea of having different types of phasers. Klingon phasers were made slightly less powerful, and their role evolved into an offensive/defensive one. Thus was made the distinction between Phaser type I and Phaser type II. But if Phaser type IIs had a defensive role, what would they be defending against?
From this, ADB developed the concept of the drone, phaser II's were designed to shoot them down (thats why the variability of the phaser II is so small compared with a phaser I), yet still afford the ship some firepower. But, we never saw any drones in the Original series, this had to be explained as well. ADB then dreamed up the idea of another bordering race away from Federation space hostile to the Klingons that used drones as their primary weapon. Thus was born the Kzinti. We never saw drones in the Original series, because we never saw any Kzinti ships. (or at least thats the rationale behind it).
Phaser IIIs came later and were designed purely in a defensive role to shoot down drones, but lacked the firepower of the phaserII (thus it only used half the energy).
As Corbomite mentions, when the game expanded beyond the two ships it originally began with (a F-CA and K-D7), they felt that ship mounted phasers were too small for starbases, which were analogous to coastal fortresses that had huge land based cannons. Such cannons are too big to mount on ships, and so ADB wanted to keep that same theme, thus the Phaer-IV was born (since they had already used the numbers 1, 2 and 3). More than likely, if it was designed from the ground up, the phaser nomenclature would probably have been reversed ie. the higher the number, the more powerful the phaser. (PhaserIs would be PhaserIIIs).