Actually it's a bit too much invasive in my opinion as well
Permissions are not invasive. What apps do with the permissions could potentially be invasive. Our apps do nothing invasive with any of the permissions. We need access to device id to validate the uniqueness of an install, we need access to device storage to store any crash dumps so they can be sent to us so that we can create a better product (we use a great product called Splunk Mint for this). Most apps require these kinds of permissions for similar purposes. If you don't like providing them, then don't install the app and miss out on a lot of fun.
BTW, we had over 1M games played in November and we didn't "invade" anyone
Any other questions?