Just to put things into perspective, the Kindle was only launched in Japan last December, though Japanese readers were of course able to buy it online from Amazon.com ever since the Kindle went international in 2009. Kobo launched their ebookstore in Japan in early July, and as you probably know that launch didn't go well. Sony has been selling ereaders in Japan since 2010.
Update: A second source has revealed that the estimated total number of ereader sold during that period was around 470,000, with Amazon accounting for an estimated 180,000 Kindle sold.
Amazon came to this market rather late, and in fact had only been selling Kindles from Amazon.co.jp for 4 months when this report was written.That makes this new estimate all the more impressive, IMO.
And even in that short time frame, other surveys suggest Amazon has already become the most popular eboosktore in Japan (with the iBookstore coming in second). The Japanese ebook market was estimated to be worth around $741 million in 2012, an increase of about 16%. It's not clear what share Amazon has of the ebook market, but I would not be surprised to learn they hold the lead.
Part of Amazon's success probably comes from the subsidized price of the Kindle Paperwhite. Amazon is selling the KPW for ¥7,980 (US$80), significantly less than the asking price elsewhere. Rakuten is matching that price with their own subsidy for the Kobo Glo, but Sony is charging a slightly higher price for the Sony Reader T2 (¥9,980).
This aggressive pricing was initiated by Rakuten, and I'm not sure that it has helped the retail giant as much as they wished. Kobo is one of the less popular ebookstores, placing 5th in a recent survey.