Can someone explain to me how this sentence even makes sense?
I'll try, and I think if you genuinely try to understand, you will. It is similar to saying that you are exporting energy when you receive bauxite and ship refined aluminum. Refining aluminum uses a lot of energy in the same sense that growing grain "uses" water; by moving it from a useful concentrated form to a disperse and less usable form, some of which winds up being recovered at a later stage, often with an additional recapture cost. So the refined aluminum, in an economic system sense, "contains" a lot of energy, even though only a small part of the consumed energy remains stored in the refined product itself.