This ebookstore is now available in Hong Kong, Malaysia, New Zealand, the Philippines, Singapore, Taiwan, Thailand, and Vietnam, bring the total number of supported countries to 36. Curiously enough the ebookstore is available in Hong Kong and Taiwan but not China.
Google is going to face competition from Kobo in the Philippines, New Zealand, and Hong Kong (edit: and Singapore), but as far as I know the other 6 countries don't have any major international competition - aside from iBooks, which may or may not count as serious competition (opinions vary).
This launch is Google's third major expansion in the past 4 months. They also expanded into Portugal and 3 other European countries in June and then came back and added Hungary, the Netherlands, and 7 more European countries in July.
At this point I think there might be a pattern to Google's expansion. They are adding new local ebookstores in regional clumps, and they also have accelerated their rate of expansion. Google has launched their ebookstore in 22 countries in the past 4 months. In comparison, they only launched in 14 countries in the 30 months since Google opened their ebookstore in December 2010.
I think Google may have worked the bugs out of their system (mostly, anyway). In recent months they've updated their acceptable format list to include Epub3, revamped the publisher's portal,and launched a new section of Google Play Books to sell and rent digital textbooks.