No, that's not a problem at all. It just the notation that's a bit weird.

For example, if e is the a-edge (first edge) from the u side and v is the b-edge (second edge) from the v side then g_{u,e} = 0, g_{v,e} = a so d_e = 0 + f(x2) where f(x2) is the flow (from Kilpatrick and Jaeger's NZ8F) on the first edge next to v.

I checked the whole thing with some surface reformulations on my side and it looks right to me.