There's no word on exactly when this will happen, but today Amazon invited app developers to start getting ready. When the expansion does happen, app developers will be able to profit from Amazon’s large customer base and e-commerce features like 1-Click purchasing, In-App Purchasing, and GameCircle, Amazon’s gaming experience for Kindle Fire.
Speaking of which, there no indication on whether the Kindle Fire will be available for purchase in those countries, but I strongly suspect that Amazon is planning to make it available to the rest of the world at the same time as the expanding app store.
BTW, is anyone else wondering just how much Amazon padded the "nearly 200 countries" claim? I do wonder, but my guess is that Amazon isn't stretching the truth all that much. If we look at where the Kindle Store is available we will likely have a good idea where the Amazon Appstore will be available.
According to the latest info, Amazon sells Kindle ebooks in 179 countries around the world. That info is slightly out of date (it doesn't include China), but I would be willing to bet that the Amazon Appstore will be available in exactly the same countries.
When that happens the Amazon Appstore will have a larger potential customer base than iTunes or Google Play. The former sells apps in 150 plus countries, while the latter sells apps in nearly 140 countries.
I doubt Apple will care all that much but Google is probably unhappy today. The Amazon Appstore is a direct competitor to Google Play, and since Amazon doesn't have picky hardware standards they have been taking away a significant part of the market that Google didn't want to support. When Amazon goes global this problem will only get worse for Google.