I usually think of the game first and then try the Zillions implementation.
The result is, sometimes, that the Zillions implementation is unwieldy. It
is true, though, that some I have not even tried to implement.
There is a great alternative, and that is our very own (thanks to Fergus)
play-by-e-mail system which is available to any square or hex board design,
requiring enforcement of the rules by the players--like a table-top chess
set.
As far as 'mentally' creating games. Yes, when the game idea is very
interesting, I find myself mulling over it and the game design works itself
out conceptually--to a large degree, however, not completely. There are
some details of playability that only work themselves out in playtesting.
Zillions is a great way to work out the playability of a game, at least as
a first step. One pitfall that Zillions has is that the farther a game is
from orthochess the poorer the Zillions engine plays the game. Some games,
it plays very poorly, some in a skewed way, some extremely well.
Ultimately, play against a person is best for testing.
If one is interested in play by e-mail, a Zillions implementation can be as
basic as a board and pieces that can move on it, without full rules
enforcement--this liberates many of the programming restrictions--since it
does not matter how well Zillions itself plays the game.
Back to the orginal question: I have found that in some practical ways,
Zillions does 'suggest' the development of a game because of the
programming practicalities. But I would not say that it inhibits ideas
altogether. There is one game I would like to try but have not found a way
to play by e-mail: Star Trek 3-D Chess (the 'real' one with the shifting
boards!) Any ideas?