How computers work is a very stretchy term. And what you need to know depends what you're working on. For example if you're scripting you don't need to know a thing about how computers work, your concerns are mostly at the software level.
If you're writing a high-performance server or a game engine, you need to understand the topology of computers. Network performance and protocols, disk, memory and cache architecture. But you still don't need to understand every machine code on the CPU.
We're risking falling into the trap of "more is more" like a chemistry teacher that is adamant that you need to absolutely understand covalent, ionic and so on bonds, because everything around you chemistry, including you. I mean how would you find a job as an accountant and start a family without understanding chemistry?
I take your point about the risk of falling into the trap of "more is more", but we're not talking about how to build NAND gates - we're talking about how integers are represented by bits and how that knowledge can be leveraged. For instance, if the author of the code showcased in the article had a bit more knowledge about how integers are stored internally, they would have realized they could have simply divided by 2^22 even if they didn't have access to a low-level bit-shift operator.
The solution in the article is a bit of a mystery. To come up with that particular solution you already know what bits are, because the first step is formatting the number as bits. Everyone, even people clueless of computers, know that computers are "ones and zeroes" i.e. binary.
Keep in mind "The Daily WTF" is widely suspected to be making up most of its articles.
If you're writing a high-performance server or a game engine, you need to understand the topology of computers. Network performance and protocols, disk, memory and cache architecture. But you still don't need to understand every machine code on the CPU.
We're risking falling into the trap of "more is more" like a chemistry teacher that is adamant that you need to absolutely understand covalent, ionic and so on bonds, because everything around you chemistry, including you. I mean how would you find a job as an accountant and start a family without understanding chemistry?