Gintama is illsuited for videogames, for lack of named finishers, sure you can see and understand Gintoki's badass style, but beyond him and Kagura, everyone else is "Slash" and one of the folowings: TsukiomiComent/Bomb/NihilisticSpeech/Bazooka/Sign.
I'd only be able to see Gintama as a Musou, where they battle parodies of other series. It's made for them Sorachi already made almost half of the fighting able character female:
Kagura, Otae, Sarutobi, Tsukyo, Kyubei, Tama, the gun girl, the evil shinsengumi girl, even Otsu Chan, or Catherine would work, the girl from the merchants
From the guys:
Gintoki, Katsura, the merchant guy with the anoying laugh, Kondo, Hijikata, Okita, the Shogun, Takatsuki, Kamui, the elitist shinsengumi guy, Hasegawa "God of Cardboard" mode, the ogre-like alien, Kagura's dad
And misc:
Elizabeth, Monday Elizabeth, Sadaharu, Cyborg Sorachi and Gorila Sorachi.
If I remembered the names of the big bads I'd start to name them, so I'll describe them: Blind Guy, Biwa Guy, Shinsengumi traitor guy, Darth Elizabeth, Obi One, Jiraia, that one big guy from Kagura's race, Kintoki, the 4 devas guy and his daugther
And the end Boss is Shimpachi feed up with everything.
But considering all the resources, and the fact that while longlasting, Gintama is a mid tier series in regards to popularity, the best that we would get is a nice DS RPG.