Games are refered to as 1st, 2nd or 3rd person in reference to the literary story telling devices of 1st, 2nd and 3rd person perspective.
In literature:
1st person is where we are having the story given to us by a narrator. We will often hear his thoughts narrated also. We are meant to be seeing the world from this character's perspective, but we still recognise that he is a different person.
2nd person literature is written with the reader as the main character, it's pretty rare tbh. I would describe Wii Sports, Kinect Adventures and other games that use avatars instead of characters as 2nd person games
3rd person we are having the story described to us as if we were a fly on the wall watching events unfold.







