A game director is in charge of the game. What makes it fun, what's new and exciting, does it look interesting, is everything balanced, and so on.
It involves a lot of talking with people. Figuring out how certain aspects of the game work. Is this character jumping far enough, why does this animation look weird, how do you make this room more like someone's lived in it, why is this hero doing so much more damage than the other, and so on. You also have to be aware of budget constraints (can we add this one more feature) and production constraints (do we have time to finish this feature). In addition to this as a Director position is one of the highest positions within a game project you'll have to answer to the publisher, go on business trips and convince people the project is worth it because this is what players want! Being a Director is about being the mentor everyone goes to when they don't know how to proceed. Reading emails and writing design documents (describing how things in the game work) are also part of the job.
To create new things. You have to have a passion for what you're doing. Not everyone is passionate about games specifically who work in the games industry (a programmer might be very interested about code architecture or an artist might be simply into amazing art) but it needs a certain craziness to fit in! That's what I love. There are few suits here. Hoodies and band logos on t-shirts are more common in this field.
The hours can be long. As it's a creative industry just like movies or music, you don't always know when creativity will strike. Thus you need to know how to progress methodically and then when you get that "a-ha!" moment you need to put in the hours to make it work. This means you can't be a person who expects to do the regular nine to five workdays. Sometimes you'll battle it out into the wee hours of the night but it'll all be worth it in the end.
To work in the games industry it's always said that you need a strong portfolio. This means more emphasis is put on showing something amazing you've made (free time or for someone else if available) than a degree in whatever. Obviously for programmers a degree bring you a long way but for an artist it's more about what you can show. Same goes for design to an extent but it's even more about being an easy person to talk to with a lot of good ideas. Learning the programs designers use isn't too hard (although some designers are more programmers/scripters whilst others are more about mood and feel), but knowing what you're talking about can't be faked. You need to really be into games to be a designer and ultimately a Game Director. Play a lot and analytically look at why things are done the way they are. The comments on the Internet and forums are not analytical and represent a minority that you shouldn't rely on when making calls (to an extent).