Pretty much every video game ever made has cut content. It's just that most times you don't hear about it, especially when many people mis-construe cut content for "the game was rushed" when it can actually happen for a myriad of reasons such as "this game mode just isn't very fun to play".
You reminded me of that scene in MGS2 where Snake tries to leave the tanker while it keeps sinking. It was shown in promotional materials and even the PS2 trailer of the game (I think). MGS2 suffered some content cut due plenty of things (9/11 controversy, rushed areas of development...among other things), but that particular scenario of running while the ship goes down was cut exactly because in words of the own developer, it was a chore, and it looked much better than how it played.