My first wrestling game was for the NES but it wasn't one from WWE. Don't remember the name but I still remember it bc back then I already knew about wrestling and got super excited when I saw the game in a store, my dad bought it, we got home, I put it in the console and got super disappointed the moment I saw it had no Hulk Hogan and no Macho Man but some guys I never had heard of and that probably just were made up characters anyways. If I remember correctly it had a Japanese guy named Hayabusa but not sure if it was supposed to be the actual Hayabusa. In the end I had a lot of fun with the game.
My 2nd one and the first "brand" wrestling game was the WWE game for NES that had actual WWE characters (Hogan, Macho, I think Bret Hart, Taker and Ted DiBiase where there too, forgot about the rest), had a steel cage and was all blue. Like everything was blue besides the characters. Loved that game.
3rd one was the WWE Royal Rumble one for SNES. That was the best one bc Royal Rumble.