Android update TextView in Thread and Runnable

The UserInterface can only be updated by the UI Thread. You need a Handler, to post to the UI Thread:

private void startTimerThread() {
    Handler handler = new Handler();
    Runnable runnable = new Runnable() {
        private long startTime = System.currentTimeMillis();
        public void run() {
            while (gameState == GameState.Playing) {  
                try {
                    Thread.sleep(1000);
                }    
                catch (InterruptedException e) {
                    e.printStackTrace();
                }
                handler.post(new Runnable(){
                    public void run() {
                       tvTime.setText("" + ((System.currentTimeMillis() - this.startTime) / 1000));
                }
            });
            }
        }
    };
    new Thread(runnable).start();
}

Alternatively, you can also just do this in your thread whenever you want to update a UI element:

runOnUiThread(new Runnable() {
    public void run() {
        // Update UI elements
    }
});

As an option use runOnUiThread() to change de views properties in the main thread.

  runOnUiThread(new Runnable() {
        @Override
        public void run() {       
                textView.setText("Stackoverflow is cool!");
        }
    });

You cannot access UI elements from non-UI threads. Try surrounding the call to setText(...) with another Runnable and then look into the View.post(Runnable) method.