I quote from the article:
As stated, long-standing inflammation secondary to chronic infection or irritation predisposes to cancer. [emphasis mine]
So what they're saying is that if you suffer from years of chronic bacterial/viral/fungal infection or irritation (due to the inhalation of asbestos etc.), that when this infection or irritation is so severe that it is accompanied by inflammation, that there is an elevated risk of cancer seen, in certain specific situations/organ systems.
So they found a link between an elevated risk for cancer in case of chronic, serious infection/irritation, so serious that chronic inflammation was caused by the condition. The article mentions that cancer can cause inflammation, to illustrate that correlation is not evidence for causation.
Chronic infection or chronic severe irritation can't possibly be compared to the short, mild, occasional inflammation caused by dermaneedling, an inflammation caused by brief mechanical stimulation, not by chronic bacterial/viral infection or long-term exposure of irritants such as asbestos.
So there is nothing to be afraid of, not even if you have infection-caused long term inflammation of the skin. Because if there was an elevated risk for cancer even with chronic inflammation of the skin, then long-term acne sufferers would at least occasionally end up with facial tumors. They don't. If years of active acne has not lead to an elevated incidency of skin tumors, then certainly dermarolling, which causes a much, much lower level of inflammation for a much shorter time, will not pose a risk of cancer.
The article is also clear that even in the extreme situations (chronic infection/irritation) from the study, correlation is not evidence for causation. So, no - dermaneedling can not cause cancer. At least there is no evidence for it, nor reason to believe it can.