Why is the DB Nav app saying partial fare for something which should be covered by the 9Euro ticket

RUF is the root word for "call" in German. It's a taxi service that must be pre-arranged by phone, essentially.

Thanks, very glad I found that information out before the trip starts.

The fare information for this is showing 9 Euro but it says that is partial fee, stating that the leg of the journey from Dombuhl to Rothenburg is not included in the ticket price.

That leg is inside the VGN Verkehrsverbund, which is an association of several transport companies, some of which are really small. Now, if one of these carriers doesn't tell DB's app makers in time that they accept a special fare ticket (like bayernticket or, as here, the 9€ ticket), the DB app simply doesn't show its acceptance, even though it is valid (just ask the driver). That Ruf-Bus replaces on weekends the regular VGN bus #807, and the 9€ ticket is valid on all VGN means of transport. Unfortunately, that incompletness of fare information occurs quite often. Over the past years, one well-known "sinner" was a company of DB itself, namely Oberbayern-Bus.

BTW, a "Rufbus" is not to be confounded with a "Anrufsammeltaxi" (AST). This is a regular cab (shared if there are any other travellers) that operates a public line at a significantly reduced fare. No Bayern- and no 9€ ticket is valid here (example for the AST operating from Dombühl with fare supplements).

Is that RUFBUS included in the 9€ fare? It's probably included, but I wouldn't be worried about the cost of the fare for the RUFBUS; it's probably quite nominal. The problem, as i see it, is that you have to call a specific phone number, 09852-4043, 90 minutes before the scheduled departure time to reserve the RUFBUS. Does the person on the other end speak English? No guarantee.

If you don't want to mess with the bus, under "Change other data" then "types of transport" deselect buses and call-a-cab. Then it will show all rail connection, taking only 20 minutes longer and one extra change. Instead of changing to a bus in Dombuehl, you will change to a regional train at Ansbach, then another at Steinach bei Rothenburg

Is that RUFBUS included in the 9€ fare?

Yes (unlike the AST)

Does the person on the other end speak English?

Maby no, but that would be his and not your problem.