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There is a short reference on George Jelliss' <a href='http://www.bcvs.ukf.net/gvcg.htm'>A Guide to Variant Chess</a> webpage to Anti-Chess, as follows: <blockquote><i> <b>Anti-Chess</b> Any variant in which kings are replaced by anti-kings (which are in check only when NOT attacked). It requires an initial position with Ks under attack, e.g. the usual array on a horizontal cylinder. </i></blockquote> Which would certainly include what you describe, although the non-capturing part isn't specified, but then the description is so general that it includes any game with Anti-Kings instead of Kings.