Wi-Fi Direct is a funny beast. It has a lot of great potential with one of the more common uses to wirelessly transfer files between devices. No need to use "sneaker net" and use USB drives to transfer files. For smartphones and tablet products where it's usually not convenient to use USB to transfer files, wireless transfer may be one of the only readily available options.
Apple has done a great job in marketing this as AirDrop and works pretty well between Apple Mac and iPad/iPhone products. Unfortunately, it only works between Apple products.
In the Android world, it's a lot more confusing. Different Android products have different names for Wi-Fi Direct and also different implementations. These implementations may not be compatible with one another.
Fortunately, Send Anywhere is available allowing Android, iPhones/iPad, Chrome, PC, and Mac products to send files with each other.
In the case of the Xiaomi Mi Note Pro, even though they support Wi-Fi Direct (which they call WLAN direct), there is no easy way to native way to transfer files like with other smart phone. Click here to see how well Send Anywhere works on the Xiaomi Mi Note Pro sending files to the Samsung Galaxy S6 Edge to any other device.
The Samsung family of Android phones use Wi-Fi Direct that works seamlessly within products within the family like the Galaxy S6 Edge, Galaxy S5, and Note II.
Some phones like Huawei P8 don't lie and warn against using Wi-Fi Direct outside of Huawei brands. Click here to see how the Huawei P8 works with the Samsung Galaxy S6 Edge.