Protocultor: This is the reason:
https://www.gog.com/forum/metal_gear_series/controller_issues_thread/post16
Better use the left analog stick for movement inside the game, and remap the D-pad to the arrow keys using AntiMicro:

1.- Download win32.portable.zip (or the msi installer) from https://github.com/AntiMicro/antimicro/releases/latest . Install it wherever you like.

2.- Run antimicro.exe and press "Controller Mapping". A window where you can map a XInput controller will appear; see attached image. If this window is empty, fill the corresponding buttons using the gamepad image as guide. Then press Save.

3.- Back at the main screen, test that at least the D-pad responds to your inputs. If not, check that you've done step 2 correctly.

4.- Click on the "up" direction inside DPads. A window with a keyboard will appear. Click on the "up" arrow in this keyboard, or press it in your actual, physical keyboard. Repeat for the other 3 directions; no other input is needed.

5.- Click "Save As" and name your profile "mgs" or as you wish.

That's it; the program should be running every time you play MGS. Tested with no issues with a DualShock 4 and a Switch Pro Controller. There's no need to run it as admin, although you should try that if the game doesn't respond to the D-pad.

Protocultor: This is the reason:
https://www.gog.com/forum/metal_gear_series/controller_issues_thread/post16
Better use the left analog stick for movement inside the game, and remap the D-pad to the arrow keys using AntiMicro:

1.- Download win32.portable.zip (or the msi installer) from https://github.com/AntiMicro/antimicro/releases/latest . Install it wherever you like.

2.- Run antimicro.exe and press "Controller Mapping". A window where you can map a XInput controller will appear; see attached image. If this window is empty, fill the corresponding buttons using the gamepad image as guide. Then press Save.

3.- Back at the main screen, test that at least the D-pad responds to your inputs. If not, check that you've done step 2 correctly.

4.- Click on the "up" direction inside DPads. A window with a keyboard will appear. Click on the "up" arrow in this keyboard, or press it in your actual, physical keyboard. Repeat for the other 3 directions; no other input is needed.

5.- Click "Save As" and name your profile "mgs" or as you wish.

That's it; the program should be running every time you play MGS. Tested with no issues with a DualShock 4 and a Switch Pro Controller. There's no need to run it as admin, although you should try that if the game doesn't respond to the D-pad.