Economic damage is real damage. If you break windows, and the govt has to repair those windows, it has less money to spend on welfare and charity and doing other stuff that a govt wants to do.
You realize there's a famous essay on economy that uses precisely the allegory of windows being broken and repaired to argue that not all GDP is good. That's right, "it's creates jobs" is a terrible argument.
The checkbook must balance eventually, or at least grow in a controlled fashion. If you could add arbitrary expenses to the deficit and get +ve value out, a lot of things fall apart.
I'm not sure what else "economic damage" could refer to that isn't some sort of physical cost? If, say, an activist uses social media to incite people to blockade a road, making 10k people an hour late for work, that's up to 10k less hours of stuff done^1. That's a cost, even if it's a "virtual" one. Say x% of those people worked in healthcare, that's x00 hours less healthcare done, and that's people killed in expectation.
^1: or up to 10k people working an hour late, which is a cost in and of itself.
I might have been wrong. I thought that "economic damage" means something like release some bad press release, which wipes a lot of economic value from stock prices.
Maybe you get more window repairmen and less police, but which is better for society is still an open question.