Legolas' and Gimli's contest at Helm's Deep

[the phantom]

It appears as if they are killing for sport

Not at all, they were killing out of necessity.

Their enemies were trying to kill them leaving Legolas and Gimli with no choice but to kill their enemies. It was kill or be killed, and the fact that they kept score does not change the situation in any way (it just keeps their minds occupied and makes the story more interesting for us).