Good find! They indeed call that the piston and that count makes it 13. By definition that's what it is - the part that is actuated by gas pressure - so it makes sense. By definition an operating rod on autoloading rifles like the Garand is what we may call the charging handle. But on an AK the operating rod and bolt carrier are the same part, just like the hammer and sear. I am fairly certain they call a tappet on other guns the operating rod - like on the SKS or G36. Going from memory here so I can't be certain.
I am only concerned they will pull a stunt like they did with the FAL charging handle and "suddenly" decide the bolt carrier extension is actually an Operating Rod and therefore a new part. Again, that will take little effort to build and I would not be too worried about it either way! I suppose if they REALLY wanted to get pissy about it, they could identify the striker (#22) as another part! LOL
Based on that pic, and the already-published ATF doc, 13 is indeed the number of parts. Good for us. Easy to modify if necessary!
Here's a question - if I were to make a thicker bolt carrier extension, would that cause any change to the action? Would it possibly reduce the recoil since the extra mass would absorb some of the recoil energy? Thinking totally in terms of performance now... would be similar to reducing the size of the gas port. Could be a way to make the system more tunable... ?