I agree with Dave’s comment about the immediacy of text messaging or posting as possibly being a reason for using “say” rather than “write”.
However, we also tend to forget that the technology has gone neyond what was originally thought of as writing. The word ‘to write” still to my mind has a connotation of inscription or writing on a paper with a pen or pencil.
The invention of the typewriter created an initial change where the words “write” or “type” were somewhat interchangeable—you can type or write a letter on a typewriter (with “type” being used more to emphasize the mechanics of the process). Essentially the writing implement or means of inscription changed—but the paper remained.
Now, with a computer, the paper is eliminated so there is no real inscription taking place. The only connection with writing is the distinction between visual and aural communication. And as voice recognition software becomes more sophisticated, we may see communication that is aural when delivered and visual when received.
I think given the changes in technology, both words “say” and “write” can be seen as stretching old words for application to new technology (as with the use of the word “ship” in “ship by overnight courier").
Arguably, both are equally applicable to communicating by computer.