That Chrono Trigger video is cool, but I've noticed that they struggle with continuity issues in their videos.
In this video, the S-System he picks up starts off with a red dot sight when the enemy is carrying it, but after the main character grabs it, it has no sight. Additionally, if you watch closely when he rolls for the gun, you'll see that he's not picking up an S-System. The front triangle sight and carry handle can be seen clearly as he rolls, and once he's up against the stairs, it changes back to the S-System.