I went through a number of chess books where advice on memorisation techniques might be expected, but I did not find anything that resembles Bouwmeester's proposed technique. Below is what I found; the books are listed in chronological order, except for Soltis.
Ilya Maizelis: The Soviet Chess Primer (English translation, 2014; original Russian edition, 1960)
Opening variations should not be taken on board by "cramming", and
learnt by heart. The mechanical assimilation of a series of moves in
some line or other is perhaps not difficult, but to say the least it
is useless. (Page 373)
You should play through opening variations on a chessboard, looking
carefully into the rationale of the manoeuvres involved. You must not
simply accept on trust everything written in the handbooks; you need
to form an independent assessment of the positions that arise. You are
therefore definitely not advised to play through opening after
opening, particularly at a fast pace. (Page 376)
A. Suetin: Hoe men de opening speelt (1974; "How to Play the Opening"; originally in Russian).
In the book's last chapter, which discusses the study of openings, Suetin points out that the study of openings requires a good memory, but one should not blindly memorise as many variations as possible.
Players should find games that illustrate the variations that they have chosen to learn. Some players are better at remembering visual features such as positions, while others are better at remembering move sequences. "It is not feasible to provide a recipe that works for everyone." Players should note down their games and analyse them; they can then consult books to check for better continuations.
Max Euwe: Praktische schaaklessen 3: Openingsrepertoire (1977).
Euwe warns against blindly following what is printed in books, but offers no advice on how to memorise openings.
Edmar Mednis: How to Play Good Opening Moves. (1982) Revised by Burt Hochberg (2002).
Mednis points out that it is much more important to understand how to play good opening moves than to have memorised many complicated variations. He cites the match between Capablanca and Kostic as an example. Kostic was noted for his memorisation of openings (and games generally), while Capablanca admitted that he was no expert in opening theory. Nevertheless, Capablanca swept the first five games, after which Kostic resigned the match.
Awerbach, Kotow & Judowitsch (1983)
J. Awerbach, A. Kotow, M. Judowitsch: Schachbuch für Meister von Morgen: Ein Lehr- und Trainingswert - nicht nur für den Nachwuchs (1983; originally in Russian).
The chapter on openings was written by Judowitsch. The last part of the chapter discusses how to learn openings. It contains the usual advice about understanding, healthy opening principles and the analysis of master games, but nothing about memorisation techniques.
Alexander Kostjew: Schach lehren leicht gemacht (1987; originally in Russian).
Like several other authors, Kostjew points out that is is important to understand the idea(s) behind the main variations in one's repertoire. These can be learnt by studying a few games that use these variations (chapter I, section 18).
Sergiu Samarian: Das systematische Schachtraining. Trainigsmethode, Strategien und Kombinationen (9th ed., 2007). This is the German chess federation's official instruction manual.
The book's last chapter discusses how to choose an opening repertoire and how to collect and analyse opening variations. It does not describe a memorisation technique. However, the book's introduction recommends players to memorise and understand one or two exemplary games for each of the themes discussed in the book.
Lars Bo Hansen (2009)
Lars Bo Hansen: Improve Your Chess by Learning from the Champions (2009)
Lars Bo Hansen says it is important to have a broad opening repertoire in order to adapt to your opponent, but does not give advice on how to study openings.
William Stewart: Chess Psychology: The Will to Win (2013).
Chapter 5, "How to Study Chess", discusses how to organise a regimen for chess study. Stewart recommends a schedule with 30% tactics, 25% positional play, 20% endgames, 15% openings and 10% psychology. He also advises not to learn openings via memorisation.
Memorization of certain positions is important for any kind of study,
but really understanding the core concepts of what is happening on the
board is a lot more important than automatically knowing what response
to make to your opponent's move.
In spite of admitting that memorisation is important, Stewart does not say anything about efficient memorisation techniques.
Andrew Soltis: Studying Chess Made Easy (2010).
At last a book that is honest about the importance of memorisation.
Chapter 4 discusses "the right was to study an opening".
Soltis writes, "Every player memorizes. Grandmasters do it more than anyone else," and that "all good opening play is part memory and part understanding".
To start learning a new opening, "a good first step is to look briefly at a large number of games that were played in that line". You should not look exclusively at recent grandmaster games, since the most instructive games are often several decades old.
An alternative approach is to find a book about the opening, especially one with good verbal descriptions. Soltis has much more to say about studying openings, but gives no advice on memorisation techniques.
Update 1: Dan Heisman
In a tweet on 11 August 2016, chess instructor Dan Heisman wrote, "[I]n all my chess reading I have never read about a player using a memorization technique & most analysis doesn't require it".
Update 2: Art of Memory Wiki and Forum
Memorisation in chess was discussed in a few threads on the Art of Memory Forum:
However, the page Memorizing Chess Games on the Art of Memory wiki is still a stub.
(The thread memory techniques on Chess.com from 2011 discusses an alternative to memorising opening lines, i.e. playing lots of games in the chose opening, starting with games that are won or lost in 20 moves or less.)
Update 3: Mnemonics and Blindfold Chess
Staffan A. Svensson: Mnemonics and Blindfold Chess (2003, PDF): discusses several aspects of mnemonics and mnemonic systems that are relevant to blindfold chess.