CharlieT
You must take the route via Zurich only if getting a Supersaver Ticket, which is bound to the specific selected train(s), such as IC3 or IR37 from Basel.
The regular point-to-point ticket however covers both routes, you can see that only in the SBB Mobile app before buying, not on the sbb.ch webshop (tricked me first too).
The p2p ticket in question (valid the entire day on any connection) for 48.- full fare says:
“Basel SBB - Arth-Goldau via Zurich o Lucerne”
So that one meets the requirement “The shipping of luggage is only possible with a valid ticket for the entire transport route […]”, even if you actually travel via Lucerne.