mrwynd: I'm now running on Win 10 x64 with no issues. This worked for me after doing all of the above. To try an help any future people here's what I did:
1: I installed the game in C:\GOG Games\Sid Meier's Alpha Centauri
2: I edited the Alpha Centauri.ini file in that folder to have exactly this:
[PREFERENCES]
ForceOldVoxelAlgorithm=1
[Alpha Centauri]
ForceOldVoxelAlgorithm=1
DirectDraw=0
ds3d=0
eax=0
FastUnitAnim=0
SmoothUnitAnim=0
MainFontSize=16
InterludeFontSize=16
DisableOpeningMovie=1
Prefs Format=12
Difficulty=1
Map Type=0
Top Menu=0
Faction=3
Preferences=10111011111000011101110110110110
More Preferences=1110100111000101101000
Semaphore=00000000
Announce=111100001110101001
Rules=1101000001110
Customize=0
Custom World=1, 1, 1, 1, 1, 1, 1,
Time Controls=1
Latest Save=
Latest Scenario=
3: I completed installing Direct Play: start> type in "features" click turn Windows features on or of, when shown.
find "Legacy Components" double click on it, you will see "direct play" check it. click OK, done!
4: Set compatibility mode to Windows 7 It now starts right up and I haven't experienced any issues so far.
Thanks. Haven't played yet, but it does start fine now.