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First let me mention that Pritchard's Encyclopedia of Chess Variants
includes an article on this subject, written not by Pritchard, but by Tom
Braunlich. It's under the entry 'Designing a Variant'. In this short
article, Braunlich describes two criteria: elegance and balance. These are
two criteria I had an instinct for as early as Cavalier Chess, though I
hadn't formalized my thought on the subject. 'An elegant game', he
says, 'combines minimum rules with maximum strategy.' To give one
example from my own games, Metamorphin' Fusion Chess combines the rules
of two other games, Metamorph Chess and Fusion Chess, and the result
transforms the strategy of the game. Unlike its forebears, Metamorphin'
Fusion Chess allows you to increase your material through reproduction.
Now let me contrast that with another of my games that never got uploaded
to the web. Shortly before Jason Whitman introduced a game called
Evolution Chess, I had created a game called Evolution Chess. My Evolution
Chess was completely different. In my game, each piece had a double set of
chromosomes, which is what determined its powers and its gender. Instead
of making a regular move, a player could mate a male and a female piece,
to procreate a new piece whose DNA was a random mixture of the two with
some chance of mutation. I suppose I should release it with an alternate
name such as Procreation Chess or Sex Chess. Anyway, as elegant as both
games are, I think that Metamorphin' Fusion Chess probably handles
procreation in a more elegant way. Procreation simply follows from the
rules, whereas procreation is explicitly built into the rules of my
unpublished game. In general, it is better when the strategic elements of
a game simply flow from its rules instead of being built into them. 

Braunlich describes balance as being between pieces. He points out that
changes in various parameters can upset the balance between a game's
pieces, and these 'must be reconstituted in some way to prevent the game
from becoming too straightforward.' A game that is too straightforward
would be one that has too much clarity and not enough depth. So he is
getting at something of the same thing as Mark Thompson writes about. As
an example, let me compare Cavalier Chess with an early version of the
same game. In Cavalier Chess, most pieces get additional Knight powers,
and the Knight itself moves as a Nightrider. In an early version of the
game, Pawns were replaced by Knights. This made the game too
straightforward, for the Knights quickly captured each other, leaving the
other pieces too easily exposed to each other. I fixed this by replacing
leaping Chess Knights with the lame Knights used in Chinese Chess. These
could be used for blocking, which allowed the powerful pieces behind them
to be used more strategically.