I used to use a DualShock 4 controller, but since it was in Bluetooth mode on my Windows PC, it displayed the controls as Xbox One controls. As you stated, the best method to get it working is to download something like InputMapper as a workaround.
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I forgot to mention that to get controller support for D2 on Steam, you need to go in to Big Picture mode, click the gear on the top-right, then click Controller Options. You have to disable all of the options that list a console as well as the generic controller support and Steam Controller. I had this problem a while back and posted on this forum too, and someone told me to do these exact steps. My Xbox One and DS4 controllers have been working like a charm ever since.