There is actually quite a bit of blood in the game.
The only censoring available in the game is the option of whether or not you want to play the "No Russian" level which involves massacring hundreds of innocent civilians in an airport, which is why the option is given since some people might find it traumatizing or shocking for a game. Might've been worse if they had put in children in there too.
So yes there is blood in this game. There are blood splatters and stuff too. Every time you get injured in the game you have blood grape jelly jam resembling blood smeared on your screen too.