I think you've confused somewhat in the UCI. Your reported results is invalid. Either the engine has a bug or you've done something wrong. The command you give is correct but the bestmove it reports is invalid because it's white to move in the final position.
When I did the same thing on Stockfish, I have the following. Please note that the first move in all PVs are white's move.
info depth 16 seldepth 24 score cp 103 upperbound nodes 2601011 nps 207169 time 12555 multipv 1 pv d4e5 f7f6 e5f6 g8f6 b1c3 f8b4 f1d3 d7d5 e4e5 d8e7 d1e2
info depth 16 currmove d4e5 currmovenumber 1
info depth 16 seldepth 26 score cp 131 lowerbound nodes 3046457 nps 207807 time 14660 multipv 1 pv d4e5 f7f6 e5f6 g8f6 g1f3 f6e4 f1c4 b8c6 e1g1 f8e7 b1c3 e4d6
info depth 16 currmove d4e5 currmovenumber 1
info depth 16 seldepth 26 score cp 131 nodes 3094910 nps 208061 time 14875 multipv 1 pv d4e5 f7f6 e5f6 g8f6 g1f3 f6e4 f1c4 b8c6 e1g1 f8e7 b1c3 e4d6
info nodes 3094910 time 14875
bestmove d4e5 ponder f7f6
EDIT:
Your question is a bit unclear because you ask for the evaluation for the move g7-g6. But this evaluation term is extremely unclear. From your comments, you're actually referring to the how well the move g7-g6 is relative to other moves that you can make in the same position.
If my interpretation is correct, your closest is multi-pv. Multi-pv lists the moves from best to worst. If g7-g6 is the second best move, you'll see the score and you can compare it with the score for the best move. I said it's closest because if your move is not one of the best moves, you'll find it hard to see in a multi-pv output.
UCI protocol is designed for computer vs computer playing, not really designed for human analysis like you described in your scenario. If you really want to know about your move. You have to play the move, get the score of it. Take the move back and find the best move in the position.