I'm reminded of the fable (in Nick Bostrom's Superintelligence) of the chess computer that ended up murdering anyone who tried to turn it off because in order to optimize winning chess games as programmed it has to be on and functional.
(Obviously closed, specific tasks like "land this particular rocket safely within 15 minutes" don't always lead to this, but open ended ones like "manufacture mcguffins" or "bring about world peace" sure seem to.)
This one becomes especially dangerous after the 15 minutes have passed and it begins to concentrate all its attention on the paranoid scenarios where its timekeeping is wrong and 15 minutes haven't actually passed.
Which pretty much tackles these issues head on.
There are interesting videos on the subject on Robert Miles channel on AI safety: https://www.youtube.com/channel/UCLB7AzTwc6VFZrBsO2ucBMg
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.