I'm not going to invite my friend to play a game
Why won't you invite your friends over to play a game?
I have other plans.
It is good to do things with friends, but you have to honor prior commitments first. Make plans with your friends another time.
I intend on playing with other people not my friends.
Well if you had plans with them you should cancel and let them know. They could feel betrayed you wanted to play with other people and not them.