How to update Google Play Services without having a Google account? I have installed an app which apparently requires a newer version of Google Play Services. How can I upgrade these services to a newer version without having a Google account?

This is on Android 4.4.2.
You will need to goto a 3rd party website that hosts Google apps and download the newest (for your device) version. The one I use is  http://gappsandroid.blogspot.com/ , you can download EVERY single Official Google app.