No, the LOS does not extend to G4 or G3.
The LOS to G3 crosses the E3/F2 wall hexside, and a wall hexside blocks same-level LOS when neither the firer nor the target is part of any of the two hexes it straddles. Similarily with G4, where the LOS crosses the E3/F3 wall hexside.
However, if you from the example removed the railway that goes between hexrows E and F (and only keep the one between D and E), you'll have clear LOS to those hexes from D2. Now, the only wall hexside crossed to G3 is the D2/E3 hexside, which is part of the firer's hex.