shuwt literally means to go to and fro or to run about. It's closely related root (as a pun) 'suwt' means to turn aside, swerve, or fall away.
Here is my bias in answering the question:
I believe that God created the only and true Mystery religion.
As such, The tree of Life is Christ himself who is the "water, water" or the Living Torah of God in heaven and on earth. What is proposed in the article is a variant of Gnosticism where John has been given a higher knowledge as he goes to and fro.
In all mystery religions there us a way to gain additional meaning from a given text. However, the constraint of that additional meaning is always in the hands of an expert priesthood.
In God's mystery religion, the mystery has been revealed in Christ, and the meaning of the hidden text is so self-correcting that children can discern the truth.
If the meaning of going to and fro, as the article states, means:
"Rather, this "going" (or "running") is of the spiritual type, and can mean both, a) angels carrying out the will of God (descent), and, b) people "connecting" with God (ascent) in terms of gaining insight into the mysteries of Torah."
Then when Satan said he had been going to and fro upon the earth, was he doing God's will? Certainly not in any immediate sense, but perhaps in a more esoteric manner. Was he gaining insights into the mysteries of the Torah? Probably not. Where is the 'control on the meaning'? In the hands of those who say it is so.
So I am doubtful of the meaning they propose.
Literally it probably means they ran around, not knowing where to settle. This behavior is uncharacteristic of one who trusts God. Figuratively, it probably means that they were falling away from God (same as the literal, but from a different direction).