"... they really hadn't experienced life in the real world because they never went out therefore establishing that they were lazy and basically didn't want to associate with anyone, therefore not enjoying the surprise."
The highlighted words belong to a pattern that John has recently discovered, and which he's trying out in this paragraph. Like many grammatical growth-points, it's tied to particular words which the learner reads, notices and remembers.
The three-word sequence "therefore establishing that" is the kind of phrase KS3 students could encounter in a number of texts, such as this one which we found on the internet: "Microsoft's lawyers duped Mike into demanding a large sum of money to give up the site therefore establishing that he only created the site for the purpose of profit and not for his own personal use."
And here we have the two-word sequence "therefore enjoying" on another internet site:
"It is also available for almost all devices and systems, therefore enjoying the advantage of cross-platform support."
For all we know, John had read and remembered these particular sequences; there is plenty of evidence that we can and do remember "chunks" of language like this. However, we would guess that John has also just noticed the similarity between such examples, and worked out that "therefore" can be used before any old present participle ("establishing" "enjoying").
This is the world of real grammar, where an underlying principle is being applied creatively.
What we shouldn't lose sight of is the real pleasure that John gets from displaying this new tool. He's expanded his expression, shifted his vocabulary up a gear, and begun to embed a new grammatical construction in his writer's toolbox. It's a reminder of the creativity and liberation grammatical knowledge brings to our expression.
On the other hand, John still has a lot to learn about "therefore" + present participle. His two examples don't really work. We'd have preferred finite clauses in both cases (" ... they never went out, which shows that they were lazy .... That's why they didn't enjoy the surprise"). But would you underline his examples and write "clumsy" or "pompous" in the margin? Or would you write "well done!" (to show you've noticed) and let time and experience do the rest?