I looked around for info on your controller and there wasn't much to be had.
If your confident the controller is working but the game refuses to acknowledge it's presence...
I'd assume it's a situation like this:
Most PC games are designed with Xbox controller support in mind. As a result some gamepads don't work or don't work optimally (i.e. default button maps are way off).
What works for most people is making your PC think your generic Gamepad is an Xbox controller.
https://github.com/x360ce/x360ce
http://www.x360ce.com/
Pinnacle costs money but they do something similar. Doesn't seem like they have GW2 listed but might still work. I've personally never used it.
http://pinnaclegameprofiler.com/
There are various programs out there like Xpadder, MotioninJoy, JoyToKey, AntiMicro etc that will map keyboard/mouse actions to a gamepad. That's an alternative route but it might not be ideal for things like the thumb sticks, I've never tested it really.
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If this Doubleshock controller is recognized as a DualShock controller; perhaps the software specifically made for DS's to emulate Xbox controllers on windows will work. I have used official PS controllers on PC but had to masquerade them as Xbox controllers to work optimally for most games.