Could anyone here be able to explain gambling addiction and its debt with Microeconomics theory?
It seems to me that the topic is related to rational addiction: Individual preferences for consuming $x_t$ are conditioned by their past consumption $x_{t-1}$. See for instance:

Becker, G., and Murphy, K. (1988). A Theory of Rational Addiction. Journal of Political Economy, 96(4), 675-700.