The newspaper headlines exaggerate the paper's conclusions, but they, in turn, are not justified by the data shown
The paper itself does not make any attempt to measure the occurrence of specific dementias but uses a standard test for cognitive performance to measure its outcomes:
The current study examined the shape of the association between alcohol consumption and change in cognitive performance.
So we could argue that the newspapers have distorted what the paper said by claiming a link between alcohol and dementia. But the initial discussion muddies the waters by starting like this:
The neurodegenerative effects of excessive alcohol consumption are well documented. Alzheimer’s disease and dementia have replaced ischaemic heart disease as the leading cause of death in England and Wales, and death rates for neurological disease are increasing worldwide.
Hence creating a link in readers' minds even though they also acknowledge in their introduction:
...light to moderate alcohol consumption is a positive predictor of health status in older adults, protects cognition and may reduce the risk of dementia in later life...
The paper then justifies its work by claiming that protective effect of alcohol is controversial. So they have piqued media interest by mentioning a big modern fear, dementia, though they are not really studying it. Good for getting attention, bad for clarity of communication.
The specific conclusions of the study were:
UK department of Health guidelines are that drinkers should not consume more than 16 g/day to minimize the risk of alcohol to health. Our findings suggest that to preserve cognitive performance 10 g/day is a more appropriate upper limit. This would translate into not more than one UK standard unit of alcohol each day.
But as David Speigelhalter points out:
Just a quick look at the academic paper’s Figure 1 (reproduced below) suggests the authors’ conclusions are bizarre, to say the least.
The response times improve rather dramatically with increasing alcohol consumption, down to a minimum when daily alcohol consumption is around 16g, which is exactly the two units a day under current guidelines. Then there is a (rather gentle) slowing in reaction times for increasing consumption up to very heavy drinking. The confidence intervals are very wide, but the estimated response time at two units a day is clearly estimated to be lower than at one unit a day, so if anything the study supports the current guidelines.
So the conclusions that one unit a day is preferable to two units do not seem in the least justified by the fitted model, and may have arisen from a misinterpretation of the curve-fitting technique [which produces kinks in the fitted curve that are not in the original data]. ...
And in fact a more suitable headline might be: drinking up to current guidelines linked to improved cognitive performance.
The paper seems rather over-eager to demolish the well-known J-shaped curve between alcohol consumption and health (see this previous skeptics.SE answer). But in doing so ignores problems with its own evidence. error bars are wide and potential confounders are problematic (not least the issue about the reliability of recall as a way of measuring actual alcohol consumption).
The actual data (as opposed the the conclusions given in the article summary) suggest that drinking moderately substantially improves cognitive performance and that this benefit only declines slowly with much larger alcohol intake.
I don't think the headlines this story created were caused by poor journalism (for a change). The paper itself courts confusion and, more importantly, makes claims even its own data do not justify.