I do feel this may indeed not be a useful MO question, because it may be impossible to answer without the details, and it would be inadvisable to give very many details in a public forum.
As for my opinion, I think it would be ethical to tell the author that you're working on a related problem in another field (without giving further details), and ask him for further explanations of his results.
]]>First, I think that this is an appropriate question for MO, although I may be in a minority. (I am less concerned about appropriateness than many other participants on the site.)
Regarding your actual question, can you find someone (perhaps someone at the same career stage as you) with whom you can discuss the results you are trying to understand? There are probably lots of other people besides the author of the paper who could explain them to you, and asking younger people may be easier for you. (For example, if you do decide to enter into a collaboration, it may be more pleasant to collaborate with a peer rather than with a much more senior colleague.) Also, you are not obliged to share your results. Whether you want to or or not is up to you; while it may make it easier to find someone to explain the results to you if you share your motivation, it is quite understandable that you don't want to share your partial results.
]]>