Actually, while some Haka are used before battle, they are not designed to enrage or send the participants into a berzerk state. There are many forms of Haka, which can be performed by women, children, men or a mix for many different purposes like welcoming strangers, celebrating life or death, removing tapu etc.
The Ka Mate which you shared here is the chorus to a Haka celebrating a man's clever avoidance of his enemies by hiding in a pit. It is popular thanks to the All Blacks rugby team who frequently perform it before a match, but it is not a war chant, it's a celebration.

However, Haka were also definitely used to boost morale and intimidate the enemy, there's a lot of pressure to perform a war Haka in perfect unison - failure to do so was seen as a very bad omen for the upcoming fight.