Short answers, pulled from the story.
Two separate awards were given at the 1st Annual Interactive Achievement Awards in 1998. GoldenEye 007 won the console award, and Quake II won the computer award. Both original categories were later retired, with the unified Action Game of the Year introduced at the 11th Annual in 2008.
Ubisoft Montreal holds the record with 6 wins from 14 nominations, more than any other developer. It is also the only studio to win more than one action-related award for the same game in the same year, which Prince of Persia: The Sands of Time achieved in 2004.
The unified Action Game of the Year category was introduced at the 11th Annual Interactive Achievement Awards in 2008. Call of Duty 4: Modern Warfare was the first game to win it.
Call of Duty has received 12 nominations, more than any other franchise in the award's history. Its 4 wins are also the most for any single franchise. Tom Clancy's is second in nominations with 10 and has 3 wins.
Hades II, developed and published by Supergiant Games, is the most recent winner. The original Hades also won at the 24th Annual in 2020, making Supergiant Games the only developer with multiple nominations to have won Action Game of the Year with every submission.
Activision and Ubisoft are tied with 6 wins each, the most of any publisher in the award's history. Activision reached that total from 23 nominations and Ubisoft from 20 nominations.