There are probably legitimate reasons to consider a variety of approaches to be scientific methods, given the differences in sciences, but I was thinking primarily of the so-called hard sciences. I belive a fair rendition of the scientific method for hard science would be:
1. Observation / evidence gathering.
2. Creating or chosing plausible hypotheses as to what has been observed and gathered.
3. Designing experiments to support or eliminate hypotheses.
4. Carrying out the experiments.
5. Evaluating the experimental results, including statistical analyses of multiple test runs, to determine which hypotheses the observations and evidence best support.
That would be asking a lot from a game, but surely someone has at least taken a shot at it.
So you'd need a game that has...
a) several possible strategies for winning/getting ahead.
b) limited random element, so the experiments are repeatable (to a degree at least).
c) logical or at least predictable outcomes from events during the game.
d) identical starting position for the experiments to be repeatable.
e) simple enough rules.
f) probably a few more points that escape me at the moment.
Anything short of 100 games of chess against same opponent, I can't think of any one game that does it all...
EDIT: Admittedly, I recognised four games from the mensa-list, so I might just be ignorant of any such game.
-jh