I believe you that they are actually played games. But you probably know that most of the extant game scores of European chess prior to the 19th century are composed games, especially in handbooks written to teach the game (for example ALL games of Greco are compositions). Also the oldest extant game scores of Chinese Chess are from such handbooks and are assumed to be compositions. So my assumption was not THAT farfetched. I do not know though if this "strange hobby" as you call it was common in Japan also.
And again, I never denied that Chu Shogi was a popular game. But I'm still not convinced that it ever was more popular than the smaller one.
So from which time are the first extant Sho Shogi game scores? Do you know that?