The author does not understand how science works. We don't "know" anything from this study. Theories can be developed, but nothing can be concluded as factual with this data. In fact, the entire article is full of contradictory statements. Like later, there's a quote from the researcher that specifically says that they don't know:
“Another explanation could be that smoking causes inflammation in the brain, which in the long term can damage parts of the brain and lead to various mental disorders. But as I said: We don't know for sure as yet."
Another issue with this is that they're conflating "being admitted to a hospital with a mental illness" with "having a mental illness". Those are not the same statistic. I'm not sure how it is in the UK (where the patient data was pulled from), but I imagine that they don't exactly have the greatest access to mental health services, as is the case with most places these days. In the US at least, being hospitalized for a mental illness is basically a last resort, often times only made available to somebody after a suicide attempt or some other form of psychotic break. In the US, you're basically only hospitalized for mental health if you either:
A: Hurt yourself
B: Hurt somebody else
C: Have a lot of money, as mental health services are often poorly covered by insurance, if they are covered at all
It's not uncommon to receive a diagnosis of a mental illness way before a hospital admission, and often way after having symptoms. For an anecdote, I didn't receive my depression diagnosis until I was about 30 (which, incidentally, was the same year I started regularly consuming nicotine), even though I'd had symptoms since I was at least 15. I've also never been hospitalized for my mental health, so it's unclear how this study would categorize me, were I a UK citizen included in the dataset.
There's also the problem with the selective dataset being used. From the original paper, they seem to have only sampled data from white people. Again, things may be a bit different in the UK, but in the US there are pretty significant differences in smoking habits between people of different races, something which couldn't possibly be factored in with such a restrictive dataset. There are also racial discrepancies regarding access to mental health services in general, as well.
If anything this may show that there there's a genetic predisposition to having addictive personality traits. Which... we've already known for a while now. Much like depression and other mental illnesses, those are commonly hereditary conditions. This author doesn't seem to be aware that correlation does not equal causation.