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'Overall, the literature of chess variants demonstrates a random
scattering of 1000's of the infinite possible, stable [not in every
case!] arrangements of gameboards, pieces, rules, etc. Despite the
constructive intentions, hard work and abstraction by their various
inventors, statistically it is as if the population as a whole which
created this class of games did so with little guidance of intelligent
design. Virtually all of these games could have instead been randomly
generated by a computer program designed to intentionally create chaotic,
messy chess variants. This is the fate of all work undertaken without
correctly applying the most important game-design principles.'

Symmetrical Chess- Description
http://www.symmetryperfect.com/shots/descript.pdf
See section 'blueprints for incredibly bad inventions'- page 5.
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Although I prefer to colloquially express a permutations analogy 
['arrangements' is the keyword clue] instead of a number theory analogy,
there is an implicit overlapping and agreement of ideas.  I am especially
convinced of Muller's observation that 'invention' is commonly used in
an exaggerated or false manner within chess variant literature.  In my
opinion, 'discovery' is usually a much more appropriate and factual word
although I consider even its usage in some cases to be melodramatic.

For a hypothetical example ...

1.  Imagine that a person flashes thru all of the 12,000+ opening setups
of CRC (discovered by Reinhard Scharnagl) and notes which ones, by quickly applying simple quality criteria, are especially stable.

2.  This person eventually completes a short list of, for example, the 24
best (by his/her criteria).

3.  This person arrogantly and irrationally imagines himself/herself to be a prolific, genius inventor who has earned fame- not merely a discoverer.

4.  This person dishonestly applies for and receives US patents for every
one of his/her 24 favorite opening setups of CRC that were not already US
patented ... albeit by carefully, intentionally not mentioning CRC at all
to the patent examiners.

5.  This person takes the fact that he/she holds fraudulently-obtained US
patents for most of his/her 24 favorite opening setups of CRC as proof
that he/she is indeed a prolific, genius inventor.

[Of course, any resemblance to any real person(s) in this fictional story
is purely coincidental.]
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Would you agree to classify this person as a prolific, genius inventor?
I would not even classify this person as a discoverer.

The desire to be accurate would compel me to classify this person instead
as an intellectual property thief (only of non US-patented gameworks)
and a phoney inventor.

After all, Reinhard Scharnagl had already holistically covered the same
ground, as a discoverer, that this person falsely, subsequently staked a
claim to as his/her own solely.
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Nonetheless, I reserve the view that 'invention' can occasionally be used
appropriately to refer to a small number of highly-unique chess variants.  I also think (as Duniho) that Muller fails to give sufficient credit to
original game inventors who have somehow managed to create complex chess
variants that are balanced, dynamic, stable and playable.  After all, the
odds against creating chess variants, compliant with every quality
criteria (known and unknown), by chance or luck are combinatorically high.  Instead, they are rare, valuable examples of intelligent design done
correctly.  Eight years filled with appr. 250 failed, diligent,
attempted-intelligent efforts on my part (until only one recent success,
in my tentative opinion) have convinced me that great games are highly
unlikely to be invented by chance or luck.