The armor that Kratos wears in the rendered CGI cut-scenes were actually intended to be Kratos's armor through the game. However the PS2 lacked the power needed to make the armor look realistic enough on Kratos in-game and was cut.
Kratos' killing his family under Ares' influence is actually reminiscent of Hercules story in Greek Mythology. Zeus' wife Hera sought to bring misery upon Hercules to spite Zeus for his infidelity. She enraged Hercules to fit of rage in which he killed his wife and children.
One of the first scenes showed to the press involved what was intended to be a part of Pandora's temple where Kratos has to stay on a magic elevator through an outdoor environment while a roaring sandstorm prepares to hit. The game play mechanics were finished, and the level was almost entirely completed but the sandstorm effects just turned out to be impossible and the whole sequence ended up cut.
Some of the concepts teased in the game's unlockable bonus videos were used in God of War: Ghost of Sparta, such as Kratos searching out his mother, or the video about what happened to his brother. However they differ slightly in Ghost of Sparta.