What he doesn't say is that we're the reason they're going to be so rich. In other words, their richness is their compensation.
Natural assets such as biodiversity, and natural liabilities, such as carbon, are not owned by the current generation, because we did not create them. We have them because previous generations passed them on to us, and we are obliged to do the same. If we deplete natural assets, or run up natural liabilities, we have an obligation to compensate future generations in some other way.
It is fairly obvious that adequately compensating the future for letting it fry is likely to be a more expensive undertaking than curbing our carbon emissions. Remember that future people are likely to be much richer than we are, and so what they would regard as fair compensation would be prodigious.
If Bill Gates gives some stranger a billion dollars and accidentally pokes him in the eye with the giant cheque at the ceremony, few people would think that the fact that this person is now a billionaire is the reason why Bill Gates would owe him huge compensation.