Time Crisis was not the first Playstation Gun game, that honour went to Die Hard Trilogy.
But Time Crisis introduced the Namco GunCon(troller). Unlike previous guns, this one offered something like accuracy, and the game benefited greatly for it.
The game itself is a faithful conversion of the arcade smash, differing from games like House of the Dead and Virtua Cop in that you can use a button on the side of the gun (in the arcades it was a foot pedal) to 'duck' behind items of scenery.
The game's tough, not so much due to the accuracy required, or the difficulty of the targets to hit. But the time limits are strict, and if you don't fire fast, and accurately, you'll run our of time.