I believe these are the instructions.

Took me a bit to get working but was worth it. Gog version, set to Proton experimental,

My Alpha Centauri.ini,

Thing that finally did the trick was disabling the intro video.

    [PREFERENCES]
ForceOldVoxelAlgorithm=1
[Alpha Centauri]

ds3d=1
DirectDraw=0
eax=1

FastUnitAnim=0
SmoothUnitAnim=0
MainFontSize=16
InterludeFontSize=16
DisableOpeningMovie=1