The money comes from being a resource for anyone who needs to restore the site and use the archive as only one example. That "anyone" can be a service provided by the archive or access to the data can be sold to the person (tech or previous site owner) that wants to restore the site.

Even if for some legal reason the data couldn't be sold it could be offered in exchange for a donation.

This is not "archiving the entire web" it's archiving the type of sites (of size and purpose) that are most likely to need the service.