As another comment points out, no it isn't:
1. Nf3 Nf6 2. Ne5 Ng4 3. Ng6 Ne5 4. Nxh8 Ng6 5. Nxg6 Nc6 6. Nf4 Nb8 7. Nh3 Nc6 8. Nc3 Na5 9. Nd5 Nc6 10. Nb6 Nb4 11. Nxa8 Nc6 12. Nb6 Nb4 13. Ng1 Nd5 14. Nc4 Nc3 15. Na3 Nb1 16. Nxb1
however, it has to be white who made the last move, because with those pieces missing, black cannot have made the last move, as none of his other pieces can move until a pawn moves, and no pawn has moved