I really don't know about the cursor, but purely as a stab in the dark, I can tell you what my video settings are and hope they work for you. (I do see the cursor; OS X 10.9.5 here.)
First, run the Wineskin configurator.
The slow (but clear) way to do that is:
- right-click "Sid Meier's Alpha Centauri.app" in "Applications" in Finder, then click "Show Package Contents"
- open "Contents" > "Resources" > "game"
- right-click "Alpha Centauri Alien Crossfire.app", click "Show Package Contents"
- open "Wineskin.app"
A quicker way is to just paste this into Terminal: open -a /Applications/Sid\ Meier\'s\ Alpha\ Centauri.app/Contents/Resources/game/Alpha\ Centauri\ Alien\ Crossfire.app/Wineskin.app
(Dear people of the future: this applied to version 220.127.116.11.)
In Wineskin, choose "Set Screen Options". My options that matter are:
"Fullscreen" (not rootless/windowed)
Resolution: "Current Resolution"
Color Depth: "24 bit"
Override Wine control…: "Override"
Use Mac Driver instead of X11: OFF! (see below)
Gamma: irrelevant to your cursor trouble, but you may want to up it anyway.
Click "Done", then "Quit".
Also, my .INI file has the DirectDraw=0 and DisableOpeningMovie=1 options, as documented in countless threads and FAQs (google it). As a side effect, this lets the game make better use of the screen resolution.
Now run the game. If that doesn't bring your cursor back, I've got a couple more stabs in the dark I'd try in that situation:
1. Try the Wineskin options recommended in the wiki instead of mine: http://www.gogwiki.com/wiki/Sid_Meier's_Alpha_Centauri#Widescreen_support
2. Try enabling the "Mac driver" option in Wineskin.
It used to work for me (doesn't anymore), and honestly X11 sounds like it might fail to display the cursor due to some misconfiguration.
If the game appears not to start at all with the Mac video driver, I recommend restarting the computer before undoing that change. (Otherwise Wine leaves some processes running that prevent the game from restarting.)
3. Try some of those unofficial patches. (I haven't.)
If you ever feel like you've painted yourself in a corner with any of these changes and need to undo everything, it's always an option to restart the computer and reinstall the game.
Good luck - I hope some of that works!