The LogCat tells you exactly what is missing in your AndroidManifest.xml.
Your broadcast receiver should be declared as follows :
<receiver android:name="com.urbanairship.push.GCMPushReceiver"
android:permission="com.google.android.c2dm.permission.SEND">
<intent-filter>
<action android:name="com.google.android.c2dm.intent.RECEIVE" />
<action android:name="com.google.android.c2dm.intent.REGISTRATION" />
<category android:name="com.example.gcmnotification" />
</intent-filter>
</receiver>
And you should declare com.urbanairship.analytics.EventService
:
<service android:name="com.urbanairship.analytics.EventService" />