Looking back at the article, he probably did get one thing right and that is the connection between the motherboard and license issues on the PC, affecting both Windows itself and perhaps some gaming software he may have installed.
I have worked on software licensing at a few times in my ill-spent career, and one of the challenges is how to identify the licensed computer, yet still allow hardware upgrades and repairs? Often, the licensed software will monitor a number of items, generally the installed CPU, the HDD serial number, the NIC's mac address, and maybe RAM configuration and serial numbers of any internal cards, etc. If any one item changes it is probably allowed, but if too many change then metaphorical alarm bells ring, leading to fresh requests for authentication from the software vendors.
Since the PC was used for gaming, I would hazard a guess it may already have had other upgrades, such as maybe a new graphics card, or extra RAM? The motherboard may just have been the final straw.
However, all of that only applies to software that runs on the PC. Even if it were possible (and I think we've established it isn't), it is the last thing credit card companies would want to do, as it is generally seen as a good thing that once you have (say) an amazon account you can then use it at home, at work, on your mobile etc. And of course, you expect your credit cards to work seamlessly on your brand new PC when next you buy one.