Editor rejected manuscript claiming it is similar to a not-yet-published manuscript (that I haven't seen). How to proceed?
I don't think there is any point in writing to the EiC, if you don't want to actually appeal the decision.  I would simply send a note to the AE who handled the paper:


  Thank you for handling my paper.  I accept your decision.  I would simply like to state that the results in my paper were obtained independently, and I had no previous knowledge of the unpublished manuscript mentioned by Reviewer #4.  I will look forward to reading and citing this paper when it becomes publicly available.


Then submit your paper somewhere else, quickly (though after making any revisions suggested by these reviewers).  I would be inclined to include a comment to the new journal's editor, saying that you have heard there is a paper under review somewhere with similar results, but you have been unable to obtain a copy of the paper or any further information about it.  You could also emphasize that you have obtained your results independently of any other reseacher / group.