In this movie, "GA" is referred as "to be used with the first appeared subject". (not always, GA can be also used another way)
But in this case of "SHOGI WA chess NO YOU-NA game DESU", WA(HA) is used with firstly referred subject "SHOGI" to explain the new word "SHOGI".
There are the cases that "GA" is used with the first appeared subject (not always) and also there are the cases that "WA/HA" is used with the first appeared subject.
Then, I do not understand why only "GA" is referred to use with the first appeared subject.
I think "GA with the first appeared subject" is easy to understand only for native English speakers for some reason I do not understand.