To me, dripping requires liquid drops that travel through air or a vacuum. Maybe through another liquid if the drops cohere. But solids can't drip, and substances can sink or travel or migrate through a solid but they can't drip through it.
Is there some special geological meaning of "dripping"? Or is this just bad English?
Solids can indeed "drip". The mantle is a solid, but it still very much flows. "Fluid" means no shear strength, but fluids are not the only things that flow and flowing is separate from having a shear strength. Fluids do not behave elastically. If you stress them at all, they permanently deform. Elastic materials behave like a spring up until a point. When you stress them, they deform, but will pop back. The mantle is viscoelastic. Strain rate matters in how it deforms. When you stress at high strain rates it, it deforms, but pops back (i.e. shear waves from earthquakes can pass through). If you maintain those stresses at a low strain rate, it will slowly permanently deform. That's, by definition, flow.
This is a good analogy for what's being discussed: https://en.wikipedia.org/wiki/Pitch_drop_experiment
The reason "mantle drip" is used is to evoke a mental image similar to that experiment.
Still seems a little weird to include in an article meant for a general audience, but I appreciate that geology uses these as technical terms.
Since you know the field, can you explain what the difference is between a solid flowing and a solid dripping? Thinking about it more, my mental model of dripping requires surface tension for drops to even exist. But surface tension doesn't exist for solids, right? What defines a solid "drop" as opposed to, I don't know, just a layer or pieces?
Or am I overthinking this and it was just chosen as a silly fun word to use?