2. Google is using their name in the branding. E.g. Apple calls the iPhone just the iPhone, not the "Apple iPhone." On the other hand, Google prepends their name to all of their product names (e.g. "Google Play" "Google Now" "Google Plus" "Google Glass"), with Gmail being the only major exception that I can come up with (off the top of my head).
2. So, you think it wouldn't go after another company calling it's media webstore Play Store or Supercorp Play? Now, I don't really know about Google, but Facebook has shown that it is possible to attack other companies even for using just a part of your (completely generic) trademarked name.
The big corps like Google, Apple, MSFT, etc. will fight it out and not really worry about the legal costs. But for startups/small businesses, this can and probably will be a growing burden moving forward.
Why not ? I think it is fair to believe there is one.