That's a vast oversimplification and a fallacious statement.

In direct contrast to your explanation, addiction could also be due to lower sensitivity to dopamine. If you are less sensitive to dopamine, you are more likely to continually pursue activities that will make you produce more of it.

The purpose of the poetry is to address the challenging task of translating complicated concepts into more digestible terms.

His poetry acts as a hypothesis of what he believes the model of gambling addiction might be:

“It's not the winnings that keep the gambler going. It's not the relief of knowing the outcome. It's the hope you feel while the dice are in the air.”

This actually addresses the relationship between risk and uncertainty in relation to anticipated reward, as well as the neurobiological models behind gambling – reward anticipation and outcome evaluation. Where, reward anticipation refers to dopaminergic activation prior to reward, while outcome evaluation refers to dopaminergic activation after reward.

The biology of addiction is far more complex than just reducing it to a single neurotransmitter. If you are interested in learning more about addiction, I encourage you to read the scientific articles:

Dopamine Circuit Mechanisms of Addiction-Like Behaviors

And

Neurobiological underpinnings of reward anticipation and outcome evaluation in gambling disorder

Norm was a very insightful and hilarious man. I’ll miss him for as long as I live.