That's because to everyone but our MC, it's just a game, no one actually dies when killed in these matches. Do you feel bad when you kill people in a game? Usually not.
To be honest, there is a difference between fighting monsters who just attack and humans who strategize, and as a top dungeon hunter, he probably never had to fight people due to reputation alone. Not to mention he was massively underestimating her both as a slave to someone he deemed weaker...
Something to note is that the stream is being blocked be Alan, so nobody can even see what's happening. You can tell because the usual chat banter that would be perfect for fighting a cheater is absent.