Here's the actual wording from FAA Order N JO 7110.65, Chapter 7, section 2
7−2−1. VISUAL SEPARATION
Aircraft may be separated by visual means, as provided in this paragraph, when other approved separation is assured before and after the application of visual separation. To ensure that other separation will exist, consider aircraft performance, wake turbulence, closure rate, routes of flight, and known weather conditions. Reported weather conditions must allow the aircraft to remain within sight until other separation exists. Do not apply visual separation between successive departures when departure routes and/or aircraft performance preclude maintaining separation....
The notice you got effectively rewrites that paragraph to read:
7−2−1. VISUAL SEPARATION
Aircraft may be separated by visual means, except in cases involving the A388, as provided in this paragraph, when other approved separation is assured before and after the application of visual separation. To ensure that other separation will exist, consider aircraft performance, wake turbulence, closure rate, routes of flight, and known weather conditions. Reported weather conditions must allow the aircraft to remain within sight until other separation exists. Do not apply visual separation between successive departures when departure routes and/or aircraft performance preclude maintaining separation....
I.E., CONTROLLERS cannot request that pilots maintain visual separation if an A388 is involved. No "Traffic, 3 o'clock, 3 miles, converging, A388, do you have it in sight? Maintain visual separation."
The pilots can fly visually, but the controllers need to do the separating via radar and commands for turns or altitude/speed adjustments. Could be because of exceptional wake turbulence, or because the unusual size of the A388 makes judging separation visually a tricky proposition.