Like telephones, telex is capable of a few clever tricks. As most of it is more one-way than phone talking, telex is even easier to shoehorn into spare blips of bandwidth than telephone chat in the same way. And there's the answerback code. Lots of companies do not have a computer or a modem. The world is bigger than we thought.
Telex is easy and familiar.
Most companies have a computer with a modem, but that doesn't mean employees are comfortable with them. Telex is the status quo. Some business sectors are still grouped around networks of firms with established routines of sending and receiving telexes each day. This penalizes any individual firm that tries to upgrade ahead of whatever ponderous association decides things by consensus for that industry. Last year at Manchester Airport in Britain, I missed the last train home to my mother's village because of flight delays.