Wi-fi direct is a specfic protocal, it is not just a softap. Please see http://www.wi-fi.org/downloads-registered-guest/Wi-Fi_Peer-to-Peer_Services_Technical_Spec_Package_v1.2.zip/29561 for the technical details.
The datasheets mentions that the esp8266 supports wifi direct but there is no documentation about how to implement. They must be mixing up what wifi direct is. I searched high and low but usually people say its not supported. Over here https://github.com/esp8266/Arduino/issues/2343 it is mentioned that with freertos it is possible.
I think this is very valuable for any application when communicating without internet.
The advantages to wifi direct are that when sending commands let say from an android to the esp over a local network without internet access the user can remain connected to some wifi network. Also some newer androids have issues with connecting to a wifi network without internet access. Also it is quicker to connect.
Looking forward to comments!