"paddle" - probably from Pong, because it was "virtual tennis". Of course, "paddles" are used in table tennis. Sounds very old-school to me.
"game pak" - I believe this is part of Nintendo's PR to distance itself from previous video game associations that public had, because of the crash following E.T. - avoiding the word "cartridge", etc.
Oh, and your roommate is a putz.
Exactly, therefore it makes perfect sense. I remember seeing "PSX" and thinking, "what the hell? A new PS peripheral?" Dumb marketing-speak.