Given that we see the Greybeards and Parthurnax both write by shouting words into existence, could this be considered the traditional form of writing the dragon language?

I think that was just laziness on Beth's part, I remember them saying that the language was designed to look like it was etched into stone with claws.

And so it does. But how does that relate to how people convey the language and its use in game?

What I was saying was that in canon, they would probably write it out, the whole "shouting words into rocks" thing was probably just to save time and money on making more animations for such things.

Why would a dragon need to write anything? They talk with the voice of the wind and seem to have faultless memories.

If I had enormous, sharp claws, I would be carving things into stone all the time. To me, that seems easier than screaming whenever I needed to add something to my To Do list.

In that scenario you'd have hands. Dragons don't in Skyrim. Must say it does sound like fun.