A country that has a high GDP to me says that it must be fairly well developed in terms of infrastructure - allowing for more efficient economic activity.. People benefit from that too, not only companies, so the standard of living tends to go up whenever economic activity goes up. That's of course generally speaking, with a lot of exceptions you could think up if you wanted to.
Essentially I think it boils down to the fact that you need to make investments to create an environment in which successful economic activity can take place.. be it investments in infrastructure, the social safety net, educational instutions, or whatever. You want an environment with healthy, happy enough workers who then go out and spend their money on the stupid crap you think up in your labs or whatever. You'll also want ways to move around your goods to your customers somehow - roads, the internet, airports, etc. It's all interconnected and the more money you invest in society, the better it's going to generally be for people and companies.
So I don't think it's that people are more productive or whatever, it's just that they have more of a support network around them provided by society, such as roads, hospitals, ways to communicate, and all that good stuff. And the less you have to worry about, the better your life will be.
Look at Canada. We have highways and stuff, a couple rail lines, general peace and order, lots of people who make a good living compared to any nation on the planet, people are healthy, the economy is decent, nothing crazy is going on except for a mayor doing crack and saying inappropriate things.. A solid place to do business in, basically! A good place for people to live as well, because that just seems to go hand in hand for reasons that are not that clearly explained above, but might seem clear if you just think about it like that?
