He showed more emotion in that 1 scene than he did for the entire duration of the books. Jon Snow in the books really didn't give a fuck about Ygirtte's death. He wasn't even sure if it was him or somebody else that shot her down. He was too enthralled into the battle itself.
When he saw Ygritte's dead body, he was just "welp, there goes another dead wilding".
Here's a good illustration of her death in the books imo:
That is a more accurate representation of what went down.