From their own website:  The 1976 state law establishing the Permanent Fund (AS 37.13), states that the Fund was created:
to provide a means of conserving a portion of the state's revenue from mineral resources to benefit all generations of Alaskans
to maintain safety of principal while maximizing total return
to be a savings device managed to allow maximum use of disposable income for purposes designated by law.

I think that's pretty clear insofar as it's purpose.    To conserve for the benefit of all generations of Alaskans.    Using the principal to produce earning to fund government (like Norway did for example) is certainly one way the fund, using a POMV payment model, would provide benefit to all generations of Alaskan's, not just the individuals who happen to live in Alaska for a year, then get a dividend that second year.