Having the same problem here. Ikaruga goes nuts with my DS4; the rest of my games work without issues. Came here hoping for a fix...

Eh, I gave up on the Steam solution and just use DS4Windows. Easy enough.

Sounds like the touch pad is active. Use DS4tool, it'll emulate the Xbox controller and the touch pad will become disabled.

Perhaps you can try to adjust the controller profiles in Big Picture Mode.
- Either reload the profile for Ikaruga to "Gamepad with Camera Controls".
- Or load the base configuration for desktop mode to "Gamepad with Camera Controls". The default desktop settings tends to interfere with games.
- Worst comes to worst you can delete the controller and redo the steam controller settings.

I had some issues with double input in some other games. Reloading the profile seems to fix it.

Found a solution, like Starbug said the issue seems to be the DS4 touch pad. I went into Steam Input and set it's input to none and I haven't had any issues since.

Well, as long as this is necro'd anyway... I ran into the same problem, and it was easy to fix. Just right click on the game in Steam, open preferences -> controllers, and enable Steam input.