NOTE: now that one of the people who actually gave the talk is in this thread, I don't know if this post will be super useful, but maybe it'll still help clarify things? Or if Lars says this is totally wrong, I can just take it down.
I read through most of the Gamasutra talk (which was pretty interesting even for someone who doesn't develop games!), and I'm not 100% sure if I got this right. Also, I am not a game developer, in case the previous comment didn't make it clear. But here's what I think is going on in that talk.
There's two separate things being discussed: one is the integration of the Steamworks controller API, which sounds very new. That's an abstraction layer that lets you define actions in your game (and certain properties like whether it's an analog or digital action, and how the analog action should work for things like touchpads), and then leave the actual mapping to controls completely up to Steam. Most of the talk discusses the benefits of using the API, and implies that you could completely remove the controller/keyboard mapping screens in your game and let Steam handle all that on its own (assuming you're only targeting Steam).
The Dualshock 4 stuff is separate. Steam Controller remapping support will be extended to the Dualshock 4, with all its native controls (gyro/touchpad) mappable in the same way Steam Controller inputs are. For games that don't directly implement the controller API, which is most/all games on Steam right now, the Steam client is presumably doing some translation between the hardware controller and the game, either emulating Xinput/Directinput controllers or keyboard/mouse input. That support is now being extended to the Dualshock 4. Either way, not only does a game not need to care if the connected controller is a Steam Controller or a Dualshock 4 (and change things accordingly), it actually can't know because of the API abstraction. The only place where this might be confusing is how do you implement button icons in your game, but perhaps I missed a detail in the talk (button icons do get brought up, but only in the context of the Steam Controller actions specifically). Worst case scenario, you could just include multiple sets and let the player self-identify. A couple of games already do this; Rebel Galaxy is one example.
The benefits of API implementation seem to be largely that you don't have to make a control binding interface anymore if you don't want to (and don't need to sell your game outside of Steam), and that even if you don't want to tie yourself to Steamworks, you can abstract some of the input functionality and then polyfill the abstraction layer for the GOG/DRM-free/Uplay/Origin/etc. release. It would be interesting if it also meant for users that the actual action names showed up in the Steam Controller setup interface, i.e. instead of assigning "Dpad Up" or "X Button" to controller inputs, you could map "Jump" or "Open Weapon Wheel" because you could send the actual names of the actions through the API to the Steam Controller interface. But that's a guess; I don't actually know if that bit has been implemented.