I don't know what you really meant, but the company's name is indeed written as アタリ in Japan. I don't know whether that's in the official logo in Japan though. And yes, Atari IS a Japanese word, as it was intentional to use Iga (Go) terms (Atari is like "Check" in chess) as their company name, and so is their subsidiary Tengen (the dead centre position of an Iga board).
I don't know how legitimate the bag is, but simply googling it says it's at least officially licensed everywhere.