No, there's no ending FMV. It's a fairly old game now. They were concentrating more on the "making this game awesome" than "making it have a coherent plot" I remember.
Doom: Knee Deep in the Dead - text. The Shores of Hell - text and a picture of hell. Inferno - text and panning across a picture, eventually leading to a severed rabbit head. Thy Flesh Consumed - text and then a picture of the Doom marine infront of a burning city, still holding that dead rabbit.
Doom 2: After you beat level 30, you get some text, then it shows a picture of the big demon you killed. Infront of it it starts showing all of the monsters in the game. With their names infront, and you get to kill all of them.