Here are some of the things I've learned that relate especially to business and management:
There's no substitute for taking a lot of actions. Every good pro StarCraft player has really high APM. Even players who are famous for being pro despite having low APM are ways faster than most people (SjoW--probably the most well-known and successful low APM player in SC2--has APM of ~130). Sure, you need to be smart about which things you choose to do and precise with your actions. And you can win some games by being smart, but almost any strategy you want to execute can be executed better by adding in more APM, whether this means taking a few units to do some harassment when you otherwise wouldn't, or just doing a better job target firing the right things in the middle of a big battle. In life, it's pretty much the same thing. No matter how smart you are, your effectiveness is going to be limited if you aren't talking to lots of people, sending lots of e-mails, and just doing lots of stuff every day. Don't underestimate how much value there is in doing whatever you are doing faster so you can move on to doing more things.
Macro is usually more important than micro but at critical moments, micromanagement can mean the difference between massive success and disastrous failure. For example, if you are making a movie, building a great team of actors and other people to work on the movie and getting enough funding, etc. is generally going to drive the success of the film, but if there's just something off about the story, then the movie can fail so that's something that might need good micro. (Star Wars I-III could be considered examples of this.) For a StarCraft example, see 8:30 - 9:30 into InCa vs. Rain M4 Set 1 here: http://www.gomtv.net/2011gslsponsors3/vod/65174 for an example of having a good strategy and good macro but then screwing everything up with bad micro at a critical moment.
There is usually more than one way to accomplish something. For example, you can deal with tanks with either chargelots, warp prism bulldogging, immortals, or lifting the tanks with phoenix. Context means a lot. The map and situation will make different choices better and worse but it doesn't necessarily mean anything definitive about any particular choice in the abstract. In life, there are usually multiple paths to the same place. If you want to be a Super Bowl winning quarterback, you can either go to a big name program (like Tom Brady at Michigan), maybe not get much playing time but be surrounded by top notch coaches and teammates and competition so you're well prepared for the NFL, or you can go to a smaller school (like Ben Roethlisberger at Miami of Ohio) and be "the man" for 4 years, get to throw a ton of passes, and generally get a ton of good practice and attention. In most things, there are a lot of wrong ways to approach a problem but still usually more than one way that will work.
Timing is critical. For example, Loopt had a lot of the same ideas as foursquare, but started before location services were ubiquitous and commoditized on mobile phones, and so they spent a lot of time doing stuff like striking deals with carriers that turned out to not be that valuable for them, whereas foursquare was able to just focus on iPhone (and later BlackBerry Android) experiences. In StarCraft, timing a push exactly to maximize your advantage is one of the most important principles of the game. Relatedly, you can never get back wasted time. If you forget to build a probe for 15 seconds, you'll never be able to catch up to someone who is executing the same build perfectly.
Execution is first order more important than strategy but there's also a ceiling on how well something can be executed, and then strategy matters. When competitors are all executing at a similar level, strategy can make a huge difference. For example, Microsoft and Apple were both executing pretty well in the personal computer business in the 1980s and early 1990s, but Microsoft's strategy turned out to be better for the market at that time. Apple is now executing well on iPad and iPhone and laptops with a strategy that looks a lot like its strategy for the Macintosh in the 1980s and 1990s (fully integrated experience that includes hardware and software, lots of focus on design, higher prices, less customizable but better default experience) but for the time and market that they are in now, the strategy is actually really good, and so it's important. In cases where competitors aren't executing equally well, strategy doesn't really matter much. In the case of Myspace vs. Facebook, it probably made more sense actually to start by letting anyone sign up and not restricting the site to college students, but since Facebook executed much better, it was able to close the gap in users and pass Myspace pretty easily.
Long term success is usually achieved by getting a small advantage and then using that to get some other kind of advantage. In StarCraft, this can mean something like getting map control with a mobile army then using that to expand safely, which gets you an economic advantage, which then lets you get a huge doom army which will let you win the game. In life, this might mean something like being born into a famous Hollywood family which makes it easy for you to become an actor which makes it possible for you to star in a bunch of movies which lets you get a starring role in TV show like Two and a Half Men which leads to #winning. Artois (progamer)' way of talking about this principle in StarCraft is by saying "When you're ahead, get more ahead" (as opposed to just trying to go kill your opponent).
Talent is a prerequisite for being top notch at most things, but in almost any field, no one gets really good at anything without putting in more focused effort and time than other people. This is mostly intuition but I think people underestimate how hard people like LeBron James and Cory Booker and even someone who runs the shift at an airport checkpoint, for example, work to get to the top of their game. If you read interviews with top StarCraft players like IdrA, the way they got there was mostly thinking a lot about how to improve and putting in a bunch of hours of practice.
Different people (/units) are good at different things. It's important to have the right people and put them in a position to succeed. When beginners play StarCraft, they often ask "What is the best unit to get?" and there isn't really an answer. If you need to fight tanks, immortals are great, but if you are fighting against banshees, they are completely useless. In life, it's easy to fall into the trap of idolizing individuals that are great at something important and assume they'll be the best at everything else too. Maybe the biggest life lesson one can learn from this is to put yourself in a position that plays to your strengths. It's great for someone like Kingsley who has a strangely fascinating personality to make YouTube videos but he probably wouldn't make as good of an economist or op/ed writer as Paul Krugman, who isn't particularly charismatic on video.
Relatedly, groups can perform better if they are made up of complementary kinds of people. In StarCraft, for example, zealots plus marines are much stronger than just zealots or just marines. In life, this is true too. The nursery rhyme about Jack Sprat and his wife is an example of how this plays out in couples.
JACK Sprat
Could eat no Fat,
His Wife could eat no Lean;
And so, betwixt them both,
They lick'd the Platter clean.[1]
If you are better than your competition, you want the game to go on longer. The more decisions there are, the greater the chances that the better player will win. In StarCraft, this is why many very strong players like IdrA prefer to play macro games rather than short rush games or cheeses. Hussein Kanji has a pretty good discussion of how Microsoft was able to win consistently in the 1980s and 1990s by taking a much longer term view than their competitors here: Hussein Kanji's answer to Why has Microsoft seemingly stopped innovating? .
It's not one big thing but a bunch of little things that add up. Most games in StarCraft aren't like the InCa vs. Rain game I linked to above -- they end up being won because one player is able to squeeze out a few more workers and a few more units and get a slightly bigger army that then lets him/her roll over the opponent. In all the rest of these lessons, it's pretty easy to pick out some story or situation that illustrates the point but it's a little bit tricky because little things like losing a scouting probe or forgetting a chronoboost don't matter that much, but if you play enough games, you realize that all these things add up and sometimes they are really important. Life is kind of the same way. For example, if you treat people well your whole life, you'll find yourself with a whole bunch of friends later on in life and it will be a lot easier for you to be successful, whereas if you rip people off or are just unkind, it won't matter much in the short term but years later, its likely to add up to being lonely and without allies. I think this is my favorite lesson from StarCraft. It's pretty inspiring to be reminded that showing up every day and trying to do the right thing and working hard will probably matter in the long run.
[1] http://eclipse.rutgers.edu/goose/rhymes/nfat/vv.aspx