The choice of the word "Invent" bothers me here for some reason. In writing a computer program, you might end up inventing a technique or data structure, but the program itself doesn't seem to be an invention. I suppose the game rules themselves might count as an invention, but that also feels somewhat odd.
A game is a fantastic invention, literally creates a kind of world. Aiming at young people, the attractiveness of a system to perform this miracle warrants the title.
In reality, invention responds to a need and cannot be generally prescribed. Generate all numbers from 8 to infinity and there you have a representation of of all possible games. Playing them is another matter--so giving some impetus to God's own prototypes seems fitting.
Yes. Though the usual word for new games tends to be `create' rather than invent. I don't believe there's more than a linguistic significance to the choice here.
I always think of game development as discovery rather than invention. Most game mechanics either already exist, or are distilled from psychological truths.