The principle approach is still the same as for any other case interview. Just that the case question might be non-traditional, it doesn't mean that the interview format changes as such.
While the first-round interviewers are more junior and usually give time-tested standardized cases, second-round interviews on partner-level are oftenly made up on the fly. Since partners are the owners of the firm and can do/ask pretty much whatever they want, and they are usually rather smart and know precisely what they are doing - so nothing easier for them to make something up on the fly (and yes, as a partner you don't spend time preparing for interview cases...) or discuss something from a current study or just ask any other starting question.
While those cases miss the typical structure of a McKinsey interviewer-led case, your approach is still the same. You need to rigorously structure your analysis and drive the case forward. As simple as that.
Hope that helps - if so, please be so kind to give it a thumbs-up with the green upvote button below!