Kitchen dimmer dims lights in adjacent room, but not always
In case someone runs into a similar problem, here is what I found and how I fixed the fault.

In the dining room, it turned out that the L1 terminal was connected to line and C to the load. This is the opposite to what I'd expect but I think is fine electrically (do correct me if I'm wrong). Anyway, swapping them round made no difference.

What did make a difference was replacing the dimmer in the dining room with one that's rated for the load (a single LED bulb). That made the problem go away completely.

(I'd still love to understand how the dimmer was picking up what was going on in another part of the circuit though.)