Does Classic Egyptian Rat Screw have Marriages?
In the revised 2001 edition of Hoyle's Rules of Games by  Albert Morehead, Geoffrey Mott-Smith, Philip D. Morehead there is no mention of marriages and also some discrepancies with the "standard rules" you and every player I've encountered myself know today. However the latest (at time of writing) version of the Wikipedia page for the game does mention it. When one examines the edit history however, the initially created page has no mention of marriages. After viewing the edit history I found what I believe to be the first mention of marriages on the page on the version published at 22:45, 19 October 2010 under the heading of "Rule Variations". The page has been massively reformatted and altered many times since and the mention of marriages has come and gone throughout these many edits. Since I cannot access the other referenced source on the current page, Encyclopedia of Play in Today's Society, Volume 1. by Rodney P. Carlisle, I cannot conclude whether or not it makes any mention of the marriage rules especially since the Wikipedia page's rules section does not specify from which references they are drawn.

While this is purely speculation given that I cannot find a conclusive source, my best guess would be that these rules are either a regional or group-specific variant. This isn't uncommon for playing card games since there are even games based off of this phenomenon such as Mao. Since it does seem to be an ongoing debate whether to include it on the Wikipedia page or not, I think it's safe to assume that it is at least a pretty well known variant of the game.

Note: Both Wikipedia links are to specific timestamped versions of the pages, this is done in case future versions (yet again) drop the mention of marriages.