It does, but it's important to put the lottery in a historical context. When the lottery started, it was run by criminals, was corrupt and resulted in a lot of violence by competing criminal interests. By creating state-run lotteries, the situation improved dramatically. Now math is really the only way that people are cheated out of their money, you don't have warring organizations trying to control the lottery and at least the government is seeing the proceeds.

The lottery may be a horribly-regressive tax, but it's better than the situation that existed before it was legalized. It's akin to the situation with illegal drugs. If governments started selling them at a slightly-lower price and with higher quality standards, you could still argue that providing drugs to people is making them less healthy. But the situation would be better than what we have today since the states would be making the profit, we'd be rid of the associated crime and many of the overdoses that result from variable quality of street drugs.

That works for most taxes on consumer products since it's fixed and not based on income.

If two people have the same exact habit it will cost them the same amount. If I have a higher income than you I'm actually paying less relative of my income than I would with a normal tax.

This is true even not considering the social aspect of it. Some of this taxes are on addictive things like drugs (tobacco, alchool) and gambling (lottery). And one social influence of addictive behaviour is poverty.