Propritry in regards to software has nothing to do with cost. VESA the standards body for Displayport for example charges for access to the Displayport standard. You either need to be a VESA member (expensive yearly cost) or pay for access to the standard in order to implement it. Yet it is a standard, because there is a body looking after its future, a body made up of all the interested parties. Some standards are free to implement, but that isn't what makes something a standard, its about who controls, who can update it and how the future of the software is made.
AMD's mantle is propriety, because only they control its future. There is no body of interested parties, there is no intention even to pass it into such a body because AMD intends to release updates that allow direct access to their hardware as soon as the hardware is available. It is without a doubt propriety, so far based on their statements they absolutely intend to keep it that way. AMD might be saying its a standard because you can implement the driver interface for free, but they misunderstand the key elements of a standard which is that all interested parties get to participate in the future direction. AMD is misusing the word and is dead wrong on that point.
PhysX = Proprietry, as is gamesworks, as is CUDA, as is gsync.
DirectX is a little different, its clearly Microsoft's but its developed with input from AMD, Nvidia and Intel, they have some control over its future. It can't be considered a standard really but its been implemented via WINE on Linux reasonably well, so its possible to say its a standard. Its certainly a lot closer than most of technologies I mentioned.
