The fundamental band gap (the smallest band gap) is a basic materials property: It is the energy gap between the occupied and unoccupied states below/above the Fermi level in the density of states (DOS). However, the DOS does not indicate which k-points the fundamental transition occurs between (direct or indirect transition). For that, you need to inspect the band structure. However, how do you ensure that the BZ route sampled by the band structure analysis will sample the k-points at which the fundamental transition occurs? In principle, you can never be sure. But, sampling paths between the known high-symmetry points in the BZ usually does it.
So yes, the band gap you "measure" from the band structure of course depends on the BZ route you sample. You may miss the "true" fundamental gap.
I suggest you think hard about exactly how the cited work did the interfacing of different materials, and which unit cells were used, because this decides the BZ symmetries to be sampled in band structure analysis. I also recommend that you get the fundamental band gap in the DOS, to compare to those found using band structure analysis.
