Not necessarily. You started things off with "Naruto and Kushina". I just pointed out that Naruto meets his mother, Kushina in the Shippuden anime. He never meets her in the earlier Naruto anime since she is already long dead in that timeline. For all I know, your new Naruto Three Words game could be referring to the timeline after Shippuden in
Boruto: Naruto the Movie where Naruto is now a grown man married to Hinata with two children and perhaps he just re-entered his Version 2 Jinchuriki form to reminisce with his mother and momentarily "re-live" the "babyhood" he never had with his mother (She was killed while defending the infant Naruto, by the Nine-Tails demon when it attacked and tried to kill the infant Naruto). I think that it's important to keep within what is considered canon in the anime, otherwise you'll turn off some of the viewers and potential participants in the game (It's not like an "Anything Goes" type of three words game). It's all open from then on once the "stage" has been set. In a second "babyhood", Naruto can get diapered and nurtured by his mother. Maybe he can even end up AR'ed temporarily to a toddler during his stay in his Version 2 Jinchuriki form. Does that sound good to you?