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If you want to play SC2 on a gamepad I suggest you extract the game files and use vanilla DOSBox, because the Boxer packaging which comes with the game on gog has jittery controls issue which makes it impossible to play the game on a gamepad. I tried various options the config file, but it didn't help, it appears that boxer just ignores the [joystick] section. When playing in DOSBox there are no joypad issues whatsoever even with standard config settings.

It seems I was wrong about the "in DOSBox there are no joypad issues whatsoever even with standard config settings" part. I reinstalled DosBox and removed my config file and I get wonky controls in DosBox too. Another issue I have is that in hyper space the game slows down significantly for no apparent reason.

I tried the "Ur-Quan Masters" version too and though the main menu plays well with the controller the game itself fails to recognize d-pad. And since I don't have analog sticks on my controller - the game is unplayable.

Good news though is that I installed Boxer and converted GOG's SC2 to vanilla Boxer package. The game plays with the controller real nice this time. There is no hyperspace issue in vanilla Boxer either. Good times!
Another interesting thing I just discovered. In the Ur-Quan Masters version of the game you actually can use gamepad to play the game if you enable it in the control settings menu. Analog sticks vs d-pad have absolutely nothing to do with the gamepad working in menus and not working in the game.