Imagine we tracked a group of 1000 randomly picked individuals who wanted to be a brain surgeon. I don't know for sure but I wouldn't be surprised if of 1000 randomly chosen people, only 3 people managed to succeed at it after 4 years.
But no one would ever say "Study shows it's impossible for an individual to become a brain surgeon." or imply that it's just random luck to be a brain surgeon. Instead we conclude that being a brain surgeon must be very hard and require a great deal of dedication and commitment.
The reason day trading is singled out whereas brain surgeons are not is that the barrier to entry to become a day trader is very low, anyone can try to become a day trader and many people think they can succeed at it.
The proper conclusion to take from this is isn't that the stock market is pure luck or just a form of gambling... it's that one shouldn't be deceived by the low barrier to entry into thinking that they can succeed at it. It's really hard, soul crushing work to be a successful day trader in much the same way it's really hard work to do anything in life that pays well.
Some group of people are guaranteed to become brain surgeons.. the demand is there, the training is there, so it is a near certainty. In fact in the US at least, you can know very closely how many brain surgeons there can be per year. Who will fill those slots isn’t too kind to all takers. It is dedication, hard work, and luck (ie ovarian lottery).
Also the majority of those that “fail” at obtaining a neurosurgery training. If they were on the path to medical training will end up falling back to any number of high paying jobs in medicine or surgery.
This study found no one did terribly well at day trading. Random chance implies there will be some outlying outcomes, but that is a fundamentally different objective than having too many people for few slots.
Also your final paragraph seems to imply a causal relationship between how hard you work and remuneration. Hard work doesn't hurt, but luck is very important.
Which isn't to say day traders can't get those things, it's just that you stop calling yourself a day trader and start calling yourself an investor when you start to intentionally build up structural/institutional advantages.
Either daily movements of stocks are not at all like a random walk, or I am just one heck of an astronomically lucky guy. Now I do consider myself fortunate and privileged, for sure... but the amount of luck it would take to repeatedly make money on the market day after day that can fund a decently sized team of high paying engineers, data center costs/hardware costs, so on so forth... it's unthinkable.
The stock market, at least to the degree that I am involved in it, very short term market microstructure, doesn't behave anything like what economists say it does.