Presumably this is a reference to the 4-wire localtalk cables introduced with the Macintosh office in the 80s, and so with the first version of Appletalk networking. This was what was adapted for use with the PhoneNet adapters that required 4-wire telephone wiring.
Another way of putting what the manual is saying would be to say that the printer (being a serial device rather than an Appletalk device) will not work over PhoneNet. I doubt that the attempt to use PhoneNet would damage the device electrically, though trying to plug a 4-pin localtalk cable into it without one of the localtalk adapters could damage one or the other physically if you went at it too enthusiastically!
A serial cable, using the connection mentioned, is what is needed for any StyleWriter serial printer. Assuming that is what you do have, therefore, it follows that it is not truly a "localtalk" cable -- though that mistake in nomenclature is often made.
The confusion arises undoubtedly because the round
mini-din plugs looked much the same through different implementations in the Macintosh family, because the cabling in each case looked more or less identical (but was really different), and also because the ports on the machines (and even some of the cabling!) could be dual-purposed for serial and localtalk connections. It was an elegant system in the cosmetic sense, by which I mean that it did not involve the "clunky" cables required for parallel printers and such in the IBM-compatible world of the time. However, it was not especially clear-cut what worked with what, even back then when real work depended on getting it right.
