AlphaGo uses TensorFlow.
DeepMind announced the were switching over to use TensorFlow not long ago.
TensorFlow is fully open-source, you can go and read the algorithms on Github. Neural networks aren't particularly hard to understand.
The post you are responding to paraphrases the situation, and neglects to mention goal states/conditions, but is otherwise a fair summary of how neural networks work.
Neural networks, particularly the 'deep' ones, do seem to operate almost like magick. Disbelief is to be expected, but I suggest you take a proper look at them yourself, and see what they can actually do.
If you can grok Python, I highly recommend playing with the Docker image of TensorFlow, which provides a Jupyter notebook (Python in a web interface) where you can easily make use of existing pre-trained models, extend them, and/or build your own models — suitable for application to all kinds of problems / problem domains.
Siraj Raval's videos also cover neural networks in almost every aspect - from coding your own NN from scratch for digit recognition (using just NumPy), through explaining what TensorFlow is, how it works, and how to use it — along with a lot of other machine-learning algorithms, libraries and cloud services.
Many of these topics are just a 5-10 minute video (some with longer live-coding 'deep dive' follow-ups), and many of the code examples are fully functional but just a screen or two of code.
https://www.youtube.com/channel/UCWN3xxRkmTPmbKwht9FuE5A
There's also some great new videos on AI / machine learning by Google and Facebook on Youtube that are well worth a watch if the topic interests you.