It actually explains what alpha is. The line above its first occurrence it says: "In the case of polynomials". So alpha are the coefficients of the polynomial.
What you are describing is how to remove _access_ to the secret. The issue here is, that the former employee still has _knowledge_ of the secret. Hence you have to rotate the secret.
https://signalsandthreads.com/what-is-an-operating-system/