Writing was the process of using symbols (letters of the alphabet, punctuation and spaces) to communicate thoughts and ideas in a readable form.
In 2368, Sela said to Spock, "I rather enjoy writing. I don't get to do it often in this job." (TNG: "Unification I")
Starfleet officers could ask that an order be given in writing if they objected to it. (DS9: "In the Pale Moonlight")
As such information was typically presented electronically, it is likely that "writing" is used metaphorically in this case.
In 2374, Commander Chakotay chose to keep a written record of his encounter with Kellin due to her species, the Ramurans, employing a computer virus to erase all record of her presence aboard USS Voyager. (VOY: "Unforgettable")