BA did not fly to TPE (not sure if they ever did?), only flew to ICN for a short period of time in recent years so that only leaves TYO. BA is one of the only airlines to fly across 5 continents (Europe, Asia, Africa, America, Oceania) so from a continents' point of view, that is probably as "global" as it gets.
I wonder if there is any airline which has no "blind spot" of sorts if that is the threshold to be deemed global with the possible exception of Emirates? Many Asian and Middle Eastern airlines have poor coverage of the Americas (particularly Central and South, most European airlines miss Oceania, most American airlines have limited flights to Africa and the Middle East, etc.
Oh, and to me no airline should be considered "global" if it ain't flying to NCE!