The objective of the kill count game type is to kill more players than the opposing teams before time runs out. In HA, if the score is tied when time expires, the last team out of the tied teams to get a kill wins. Elsewhere, play continues and the next team to get a kill wins.
Kills are scored according to which team did the most damage over the last 10s to the character that died. When there are three teams involved, such as in Heroes' Ascent, this prevents a team from simply waiting and picking off low targets.
The kill count game type can be found when playing on The Crag map in the Zaishen Challenge, Zaishen Elite, Random Arena, and Codex Arena and when playing in Broken Tower or occasionally the Hall of Heroes in Heroes' Ascent.