I always (well, recently) thought it was because of discrete marginal utility functions.
For most people, the material difference between making $600/month or $570/month isn't much. You're still poor. You might get to splurge on one more restaurant meal a month, but that won't make you feel any richer.
The difference between having $0 in the bank and $60M in the bank is enormous, however. You've gone from poor to rich, and can do whatever you want with your life.
So for most people, the tradeoff is between certain poverty or a very small chance of escaping poverty. Squares with the article, too: by making people "feel poor", they were highlighting the contrast between their present life and the life they would have if they won the lottery.
Poor people tend to make bad decisions on things like that because of their perspective. $1/day doesn't feel like a lot of money even when you are only making $600/month. Especially when you have some fixed costs like gas that take so much out of your income.
I'm pretty sure Massachusetts is the most educated state in the country, and yet it has the highest per capita lottery expenditure (over $600 annually is spent on the lottery per MA resident!).
The science behind why people play the lottery is extremely well researched by private contractors. I worked in the space for a bit and it was pretty sad. The private contractors are very scientific about developing the most addictive products per demographic group(seriously, some scratch off cards are directly targeted at certain ethnic groups, ages groups, sexes, etc.). For instance, "Match 3" cards are aimed at poor, uneducated minority groups who find games with numbers too complex.
