"Now, usually copyright protects the copyright holder's right to earn money from their works. It is on this basis that they sue for damages. How does that sit with GPL?"
Copyright gives a rights holder a range of restricted acts; acts which only the rightsholder has the right to perform, save where there are statutory exceptions or rights (depending on how you construe various parts of the law of copyright).
However, copyright is not purely a financial issue; one need not prove loss to bring a successful action for infringement of copyright, nor need to bring a claim for damages - one can merely bring a claim for infringement, with a remedy akin to an injunction - a court demand that the respondent, if found to have infringed the claimant's copyright, ceases to do so - or delivery-up of the infringing goods.
(There are also concepts of "moral rights" (e.g. the right to be recognised as author of a work), which, intrinsically, have limited/no financial value)
One could also make a case for an equitable (discretionary) remedy of an "account for profits"; a claim akin to unjust enrichment that, through infringement of copyright, the respondent has made money which they should not have made, and which should be paid over to the claimant.
In short, when dealing with copyright, one need not prove financial loss to bring a successful case.