Google Play Services: Can't solve the SIGN_IN_REQUIRED error

Before I back-pedalled into using the clean template activity, I had manually created an app that uses the GoogleAPIClient, which resulted in the app working (probably) on my device, but not on any other.

From creating the template Google Play activity, I only changed the manifest to include the app_id that I have registered with my Google Play Service account. When launching the app it shows a brief "Logging in" popup from Google Play, then continually tries to reconnect. Have tried with different devices on different computers. Have tried with both the owner's and assigned tester accounts. Same result.

I can't use any invite or room creating services.

Here is my Manifest:

<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://ift.tt/nIICcg"
    package="com.example.kai.twincrawler" >

    <application
        android:allowBackup="true"
        android:icon="@mipmap/ic_launcher"
        android:label="@string/app_name"
        android:theme="@style/AppTheme" >

        <activity
            android:name=".TwinCrawlerActivity"
            android:label="@string/app_name" >
            <intent-filter>
                <action android:name="android.intent.action.MAIN" />

                <category android:name="android.intent.category.LAUNCHER" />
            </intent-filter>
        </activity>

        <meta-data
            android:name="com.google.android.gms.version"
            android:value="@integer/google_play_services_version" />
        <meta-data android:name="com.google.android.gms.games.APP_ID"
            android:value="@string/app_id"/>
        <meta-data android:name="com.google.android.gms.appstate.APP_ID"
            android:value="@string/app_id"/>
    </application>

</manifest>

Thanks for any help you can provide.