No, the Capital Asset Pricing Model has nothing to do with this discussion. It takes the payoff distribution of capital assets as exogenously given (and known), then makes assumptions about investors' utility functions to find the price they're willing to pay for these assets, then employs an equilibrium argument and some neat maths to arrive at a linear relationship between the expected excess return of an asset and its beta.

The concept of beta (and non-diversifiable risk in general) is related to the concept of “economic profit”.

They may not be directly related but to claim the CAPM “has nothing to do with this discussion” of economic profit is a bit strong.

Any suggestions on where one can learn more, particularly with the mathematics involved?

Wikipedia is honestly pretty good.