Goldschmidt alumino-thermic process
Actually, activity series works well in aqueous medium, while these reactions happening at high temperature will leave all waters long gone in vapours.

Well, here we go by (delta)G for the coupled reactions.
We know that a negative (delta)G amounts to SPONTANEOUS process.

The 2 reactions which need to be coupled must be such that sum of (delta)G1 for the reaction-1 and (delta)G2 for the reaction-2 is NEGATIVE.

Seeing the curve, we can conclude, Al can reduce all the metals listed except Mg, which of course could be above ~1600 degree celcius.

The conclusion: upto 1600 degrees Mg can reduce Al2O3, while above 1600 degrees Al can reduce MgO [Unlike what happens in aq. medium!]