I think this comes from the theory of general artificial intelligence where your AI would have the ability for self improving. Hence it could develop any capability given time and incentive for it.
A human mind not giving due consideration to the effects of granting arbitrarily high intelligence to an agent with simplistic morality counter to human morality.
From there it's a sequence of steps that would show up in a thorough root cause analysis ("humanity, the postmortem") where the agent capitalizes on existing abilities to gain more abilities until murder is available to it. It would likely start small with things like noticing the effects of stress or tiredness or confusion on human opponents and seeking to exploit those advantages by predicting or causing them, requiring more access to the real world not entirely represented by a chess board.
There are interesting videos on the subject on Robert Miles channel on AI safety: https://www.youtube.com/channel/UCLB7AzTwc6VFZrBsO2ucBMg