I am not convinced that adequately explains the correlation. The poor may gamble away an irrational amount of their money because they are too stressed to think rationally, but it may also be the case that the endorphin hit that gambling gives them offers them a sort of temporary escape. Gambling addiction looks, at least on the surface, to have a lot in common with addiction to substances.

I agree with your general premise, hardship probably does drive people to attempt the irrational, but I think gambling isn't necessarily a great example of this since there is likely more going on there.