On one side, yeah - the work he did will be worth a lot more than $10k to Rockstar. They've had lots of people complain about & stop playing GTA online because of the slow loading times. And this issue would probably never be found or fixed otherwise.
On the other hand, he did it for fun (without any expectation of reward). $10k isn't massive and we can quibble over the reward amount, but its delightful that companies are rewarding people at all for fixes like this. A few years ago he'd be lucky to get sent a GTA t-shirt. Its definitely the right direction we should be moving in - bug bounties are a thing in security, and we should be celebrating any movement toward rolling them out in other circumstances.
This might be an argument for him to console himself (or just keep smiling) in the event that he received nothing. It isn't a valid consideration for Rockstar, which should take heed of the calculus you stated with your first hand only, because for the beneficiary of a windfall, karma awaits.
Let us spin it differently: contact Rockstar before publishing the details of the fix, and offer to help them on this issue. How much do you believe that Rockstar would value the fix *a priori*?
The truth is this kind of fix is worth a lot, but it is always tempting for the company to be penny-pinching (and come up with justifications for being so) after the fact.
Its probably because some project manager would have told the engineer who wanted to fix this that its not important.