The President's daughter has been kidnapped and it is up to John McClane and a police companion to punch, kick, shoot, and blow their way through a horde of bad guys to save her. The game utilizes Sega's Virtua Fighter engine, but allows you to also make use of various weapons that you pick up along the way.
In Japan, the game is called Dynamite Deka.
Since Sega had a "Die Hard" license when they made this game, it bore the name and featured John McClane. When they designed the sequel, they lost the license, had to remove John McClane, and rename the game Dynamite Cop.