Include public GameManager unit tests in presubmit

Switch to use non system uid and grant necessary permission as
otherwise it will crash the test mapping (b/260071873), this was
explained in b/140028487 and a similar fix was done in ag/9523307.

Bug: b/243448953
Test: atest --test-mapping \
      services/core/java/com/android/server/app:presubmit
Change-Id: I93bcc3c9d462fb4a2f90acc5c80ae1bcbc255927