Honestly, I am uncomfortable with the idea of either Apple or Google owning the .app TLD. In its filing, quoted above, Google pledges that this “won’t be limited to any specific platform” but who really knows what level of control the company is allowed to enforce on the domain.
It may sound like abstract scare-mongering but monetisation of app marketing is a huge business. Google is currently considering paid app placements in the Play Store, for example.