The argument is that gambling houses are taking advantage of people's poor education to bilk them out of money. In principle, everyone in developed nations should know that gambling is a poor investment, but it takes good financial sense to really understand that. People with good financial sense usually aren't very poor.

So when you look at how poor people spend money, the rational economist would never advocate spending the money on the lottery. The utility is low, and even if the expected value is positive, the variance makes it a bad idea. Poor people would be better off spending money on things with greater returns.

The problem is that poor people don't spend their money on things with greater returns. They spend far too much of their money on lottery, and it's probably combination of psychological factors and financial illiteracy. I could be off on this, but I remember a statistic showing that there isn't much deviation on how much money any random household spends on the lottery. So a household with $100,000 in incomes spends as much on the lotter as a household with $20,000 in income. The result is that the lottery has become a regressive tax.

This misses the point of the article, which is that gambling should not be regarded as an investment, but as entertainement. But I agree that poor people are possibly more likely to see it the wrong way, i.e. as a good investment.

The result is that the lottery has become a regressive tax.

By the same argument you can conclude that potatoes are a regressive tax since they cost a higher fraction of the poors' revenues.

When you give money to the government with nothing in return (except as a member of the collectivity), that is a tax. Not when you give money to a private company in exchange for some kind of entertainment.