just to understand this better, the notation here is opposite to that in boolean algebra, where A*B would mean A and B, and A+B would mean A or B?
Forget about boolean algebra.
The top line " A.B-4Ω~16Ω/SPEAKER " means IF playing speaker A OR B only, the amplifier able to safely power 4Ω to 16Ω impedance rating speaker.
The bottom line " A+B-8Ω~16Ω/SPEAKER " means IF playing speaker A AND B together, the amplifier able to safely power 8Ω to 16Ω impedance rating speaker.
What is the reason behind these different ratings, i.e. what is different between the two configurations (maybe in terms of the wiring or other internal features) that would cause the different impedance rating?
Nikko NA-550 is designed to safely power speaker not less than 4Ω impedance. If playing two sets of speakers together (speaker A and B), both set of speakers are connected in parallel by the speaker switch and the total impedance apply to the amplifier will be less.
https://geoffthegreygeek.com/calculator-speakers-in-parallel/