There's basically two requirements here:
1) It doesn't assume you already know some typing
2) It looks like a game
I can find some things that satisfy one or the other but not both.
Epistory looks closest to me in terms of being a fun game. But I think it's too hard for someone that doesn't already know how to type a little, even on the easiest mode.
https://store.steampowered.com/app/398850/Epistory__Typing_Chronicles/
Most websites feel like they're for competitive typing or just getting faster a typing. TypingClub is the only one I've found that looks good for a total beginner, but it looks mostly very sterile, with games interspersed but not the main focus.
https://www.typingclub.com
I've got the kid playing Mario Teaches Typing in DOSBox, which is working out fine. It's just surprising I couldn't find anything modern that works better.