After starting alpha centauri from the gog galaxy launcher, the movie plays fine and I enter the game menu. If i try to start a game, then once it needs to initialise the game it terminates the game with the message: "unable to allocate draw buffer: terminating program". I have run the install of the directx 9.0c and tried uninstalling and reinstalling of the game. Any other ideas I could try? I am on windows 10 (64-bit) and my hardware is compatible with this game (as it worked under windows 7).

I'd suggest first, going to the .ini file for the game your running, (SMAC and SMAX use different executable) and changing DirectDraw=1 to =0.

Several, including unofficial compatibility patches.

(Note: By installing these you may void any chances of GOG support being able to help you in a meaningful way.)

Windows. 🤷

There's a reason I gave up on it firmly.

I believe you should never, ever run any DirectX 9.0c install on Windows 10. It already comes with its own DirectX. That was true even of Windows 7. I don't know if Windows is smart enough to avoid problems if you do anyways, but if it isn't, you can run dxdiag to see if your DirectX installation has become inconsistent somehow.

Setting DirectDraw=0 in the Alpha Centauri.ini has been working well for me.