The computational content of the cited paper includes two parts:
- DFT calculations (such as band structures) with QE;
- Transport calculations (such as Seebeck coefficients) with BoltzTraP based on DFT calculations.
The $8 \times 8 \times 8$ and $9 \times 9 \times 9$ are chosen for DFT calculations. However, the dense k-mesh with $40000$ points in the first Brillouin zone is for transport calculation. Why transport calculation needs so dense k-mesh is related to the semiclassical method that BoltzTraP adopted.
You may take a look at the computational method of this paper also calculated with BoltzTraP:
Hope it helps.