Simply put, it's not a closed system.
Sweden is connected to the rest of Europe. So, German, Danish, British, Norwegian, etc. grids can import and export power as needed. The entire continent of Europe produces wind (and other power) at a pretty steady and predictable pace. Power is big business since selling it in the market is pretty lucrative. And since wind is pretty affordable, a lot of the supply is wind based these days.
Basically, Sweden can produce cheap power locally most of the time and import more expensive power when they need to. Having a surplus means they export more power than that they import over time. It's just market dynamics. Because the way weather works, if there is no wind locally, that just means there definitely is some wind elsewhere. That's why Europe gets away with having so much wind power. The amount of wind power it produces fluctuates but not nearly as dramatically as you seem to believe.
It's a rapidly growing market because as you note there is plenty of demand for more power. Hence, the rapid roll out of the cheapest way to produce it world wide: wind.