The companies suing Amazon Japan requested damages of approximately 280M JPY, or approximately 2M USD. Of course, this is not a lot of money given Amazon's scale, but the companies tried to recuperate lost profits.
With that said, the discussion on Yahoo News is mostly in agreement with the opinions shared in this thread: given Amazon's scale, a fine of 35M yen is equivalent to no penalty.
Looks like it's damages and not a fine. Also, I don't know the Japanese system but lots of jurisdictions don't have a US-style concept of punitive damages. So the sum is probably what it is because it's intended to compensate those particular plaintiffs for demonstrable damages rather than to deter Amazon.