This is one of the tons of Doom clones that were released in 1994/1995.
The story: Dr. Radiaki has created an army of genetically modified creatures, and wants to conquer the world. You have to go to his fortress and stop him.
The main points that set it apart from other games in this category: it's intended to be rather humorous, you start with a baseball bat instead of a knife, and you actually have to reload guns (ie you have to hit Space almost constantly).
This was a minuscule budget game which took about seven months to make this game from start to finish.
On December 30, 1995, The Fortress of Dr. Radiaki was put on the infamous German index by the BPjS. For more information about what this means and to see a list of games sharing the same fate, take a look here: BPjS/BPjM indexed games.
Computer Gaming World
November 1996 (15th anniversary issue) –#5 Worst Back Story of All Time