I don't really like the rambling tone of the article which never really addresses it's central premise-questions.
Look, systems thinking is about thinking. Thinking is about how you were trained to think. To become a systems thinker, learn how to think better, how to think differently, how to think critically, and how to think logically. Now self-examine, correct problems, and repeat loop.
For example, the thing many elite schools teach that most others don't is the trivium and quadrivium approach to thinking.
Another trick is less tangible. Find brilliant people and learn from them. Learn what they do wrong, not just what they do right.
Finally, as a sysadmin, if you learn to think in a flowchart about just about any problem you will be fine... but the trick to that is to be specific about what the problem is.