This is something that many of even the video game designers are just now waking up to, so it's nothing to be ashamed of that many of us didn't realize it before. Still, it's important to emphasize: more buttons does not equal more intelligent. In fact, I'd argue that for most designers, it's a crutch, in precisely the way Molyneux describes -- it's extremely challenging to make a game as deep and rich as Go, so rather than try to create a robust, focused experience, they just keep adding crap on and hope the game is "deep" simply because of how many actions there are in the game. If you give a character 40 guns to work with, it's automatically deep!
There's a reason Starcraft is still on the top of the competitive gaming scene, even though it's long been passed in the sheer number of units and tech trees involved.
You raise a good point, but I don't think it's the whole story.
On the one hand, you have games that become deep through the sophisticated application/interaction of simple mechanics. "Go" is apparently one of these, and in the video game world there's... well, I can't think of any right now, but I'm sure they exist.
But on the other hand, there are games whose depth can't be separated from the complexity of their inputs. Fighting games, for instance. You couldn't make Street Fighter with one button and a waggle stick. Strategy/sim games, too, can rarely eliminate their complex interfaces successfully. These games need a lot of options to maintain their long replayability, and deep and complicated menu systems are a necessity. Even Starcraft wouldn't get by with a Wii Sports control scheme (shake once to build units. Shake twice to deploy units. Shake three times to attack...).











