Your computer most certainly supports OpenGL, although how far that support goes is... awful to check on windows (The best I'm seeing online is a third party piece of kit named "OpenGL Extensions Viewer" which will tell you the "Version" (That is, the "minimum supported version" because OpenGL is... weirdly structured for those not in the know).
EDIT: The game requires only opengl 3 (presumably .0, that's up to godot), and even then only if you run the .bat. If you just run the exe it should work fine!
EDIT2: After testing it, if absolutely nothing else works, you could grab a livecd copy of ubuntu or debian or whatever and run the game in that (either directly or in a VM or what have you, but directly is probably easier to set up)