Nope, The Terminator came first… And I don’t think that’s THE first game, either.
I only knew this because I did some research out of confusion. See, when I grew up I had a game by a company called “Bethsoft”, and I vaguely remember it being a joust clone (though I could be confusing two things). I remembered it real well because I was 9 years old and their logo was a “tastefully” topless fairy. And you know what “tasteful” means to a 9 year old boy lol
Edit, looks like their very first game was Gridiron!