People are complaining about the violence in Doom again? Number one: The creatures the player fights are hellspawn, not soldiers fighting for an ambiguous agenda that you can shoot in FPSes or innocent civilians you can massacre in sandbox games. (Might I also add that all of those are fictional, since we are talking about video games.) This is one example of a story where there is no chance of negotiating with the enemy, and they have no redeeming qualities. Whether through divine powers or lots of lead, the player is going to have to fight them.
Number two: Everything in that trailer has been done before, by the original Doom and other games. Gears of War's entire early appeal was designed around chainsawing your enemies if half. Mortal Kombat's gruesome finishers have been steadily growing more realistic looking. Plenty of games have had gory gun violence.
Yet, someone still want's to gripe about a little bit of red in one game? Fine. Let them. They have the right to an opinion. But, they will soon be forgotten by the people who will be enjoying the game, and they will turn to the next morally questionable thing they see while forgetting about Doom. It's hard to play the "think of the children" card when the demographic of most games today is 20s to 30s. (Though, the Australian government is sure to do it when they get their review footage. Luckily, imports and other methods can get around some old coots, who are so out of touch with the modern world that I am surprised they don't scream witchcraft at the simple operation of a toaster.)