You basically have the story right. (Good job!)
But you’re forgetting about the window that was lost. No matter what you do, or all the new things that get produced…no matter how you slice it, without the hoodlum committing his vandalism, you’d have all that stuff plus an extra window.
For anyone interested in resources on the fallacy, see the Mises Wiki article (in particular the links section)…
Parable of the broken window
There was quite a bit of discussion in this thread:
Discussing with a Keynesian -broken window fallacy..need some help!