This is the key point. There isn't a company on Earth that has access to consumer data like Amazon. If they've decided the gaming market is something they can get into, the decision would have been based on all of the data they've been pulling in for years on gaming habits and purchasing.
Honestly, while Google and Msft are massive companies, they don't have the cloud structure, consumer data, market saturation, ubiquity, or subscription levels that Amazon have.