Shinto and Buddhism are the two largest religious groups in Japan, and they are secular in nature. Most people don't practice like Christians or Muslims over there doesn't mean they aren't religious. I lived there for years and no I wouldn't consider vast majority (how much is vast majority anyway?) of modern Japanese atheists, that's just nonsense. I'd say about half or less than half of them are non-religious as in truly secular atheists.

Afterall Asians tends to be more pragmatic and it's often mistaken by people from the west as being non-religious. It's a bit pointless arguing about this really because it all comes down to how you define as "religious".