Under what rule of usage does this semicolon in the example sentence fall?

The use of a semicolon as a 'super-comma' to collate elements in a sub-grouped or other complex list with more clarity is probably accepted by many English writers nowadays. Thus

The groups he chose were Ali, Betty, and Clive; Dwayne, Elly and Frances; Geoff, Habib and Ian; and Jasmine, Kelly and Lily.

For other examples, see this article by Lola Taylor at Scribophile (which also mentions the changes in attitude to the acceptable use of the semicolon).

Taylor (op cit) even mentions the possibility of replacing a comma by a semicolon + conjunction. She gives an example with but; I'd say that sentences starting with and might also still be considered reasonably idiomatic. However, using a semicolon as a super-comma in other situations (here, to signal a more major sentence division than the other two commas do, with the addition of or) is highly unusual to non-standard nowadays. A dash (or full stop, and yes, a sentence beginning with 'Or') would be used today.