I'm not sure if it's the controller or the game.

The control kinda of goes in and out of working, and the directional pad shifts rapidly between working, sticking, and not providing any input a all.

Mailed support?

Probably the controller. I tried my Mayflash classic controller adapter and had problems with it automatically moving a certain direction, but my PS3 afterglow controller worked just fine.

Where do you find that?

Top right of GOG next to "My Account" is a button that says "Support".

PS3, Logitech, and most generic controllers use Direct Input. Xbox 360 controllers use Xinput.

The Logitech F series (F310/F510/F710) allow both Direct and X inputs via a switch at the bottom of the controller: D - X. Hotline Miami, for example, uses Xinput. So you switch it to X. Street Fighter Alpha 2 uses Direct Input, so you'd switch it to D.

I think that's because PS3 controllers use Direct Input, like Logitech gamepads do. The 360 controllers use Microsoft's proprietary "X input", which only came out around the time of the Xbox 360. As a result, most older games, and even some modern games, don't recognize the 360 controllers but do recognize PS3 controllers.

Doesn't work for me either on my Logitech F310. :(