Gargoyles the game actually doesn't have too much in common with the late cartoon it's based on. The player controls Goliath, (voiced by Keith David) leader of the Gargoyles Manhattan clan, on a journey to catch Demona and prevent her from using the Eye of Odin.
There are virtually no connections to the television series's storyline. Only the aforementioned characters appear in any fashion. Most of the game takes place during the first century A.D. before the titular gargoyles are turned to stone for 1000 years to eventually be awakened in episode one of the show. As such, the player defends Castle Wyvern against an army of vikings... and also giant, evil robots. Like the show itself, the game targeted young teenagers and dealt with many mature story themes rarely seen in a side-scroller at the time.
The storyline is widely considered to be non-canon.
Gargoyles plays similarly to most other 2D action games of that era. The player is essentially moving from left to right on every level and there is an abundance of platforms to jump and enemies to attack. It is worth noting that Gargoyles is an incredibly tough game, even by the standards of that time and there is no continue/save system.
Gargoyles did not fare very well in terms of sales or critical reception. As a result, the planned SNES version of the game was never released.