The study doesn't literally say "impossible" but "virtually impossible" and they do say that a very small percentage was able to make about $310 a day which is about ~110k a year.
The more interesting trend, which isn't covered in the abstract, is that profitability is inversely correlated with how long you stay at it. It was 30% of people who day traded for one day and gave up on it, and steadily dropped down to 3% for people who kept at it for more than 300 days.
As a stats person, that struck me as a very evocative distribution. The paper put it nicely: "This peculiar pattern is similar to what we would find, for instance, in the casino roulette."
The next thing I would want to know is, if you model the stock market as a machine that simply gives random payouts drawn from some distribution, what is the probability that a set of 1,551 groups of 300 random draws from that distribution would contain at least one set that averages more than $310? If the paper ran such a model, I didn't see it.
The abstract says the trader who made $310/day had a standard deviation of $2560 (presumably per day). Over 300 samples, that's a standard deviation of 2560/sqrt(300) or $150/day. So if he really had a breakeven strategy and got lucky, he was 2 standard deviations from the mean, or in the top 2.5%, and you'd expect 40 other traders to have done just as well, and it would be vanishingly unlikely that nobody else did.
Not quite what you were asking, but I don't think there's enough information at least in the abstract to answer your question. The payout distribution will be largely dependent on the size of the traders' positions and riskiness of their strategies.
In the short term it's not that unusual to flip a coin and get 5 heads in a row, but the more you throw the closer to a 50-50 split you'll see.
My hypothesis is that their average returns would end up being much higher than the returns they realized by day trading that whole time, due to less money being lost to fees.
$310 * 5 days a week * 52 weeks a year = $80,600