This Zombie enemy has quite slow movement speed, with a somewhat slow attack rate. His attack power is 40,000, which can instantly kill most of the Normal Cats, Special Cats and Crazed Cats at their level cap. His range is 600 and he has Area Attack, making his attacks devastating to most units.
Once he is killed by a non-Zombie Killer, Inumusha will revive one more time, but with only 1/4 of his original health. Unlike most other Zombies, Inumusha cannot burrow past your cats.
One of his only weaknesses is that Inumusha gets knocked back quite easily compared to most other boss enemies (every 16,000 damage taken), so he cannot push too far when not supported by something like the Zir Zeal in Multiversal Studios or the Dread Bore in Floor 43.
The character's name is a contraction of the Japanese word for dog, 犬(inu), and the cat unit's name, Musashi.
The title of the play, "Battle of Ganryu Island", refers to a legendary battle taking place at Ganryu Island, where the famed swordsman Miyamoto Musashi fought and dueled his rival, Sasaki Koujiirou, and won with a wooden sword crafted from an oar. More details can be found within the Wikipedia article.
The "Cursed Castle" in his description is most probably the Doge Base.