I frequently say that IBM sells websphere to assure that they continue to sell mainframes. Because everyone knows if your going to replace your mainframe, you need to rewrite it in java, and what better framework than one provided by IBM! Then when the whole project ends up taking 100x the hardware IBM can pretend there is some secret sauce in those mainframes.
But, to the linked answer. While the details differ a bit, the zseries is simply a low level description of how the machine worked (past tense because modern zseries mainframes have a lot of hidden "virtualization" in order to leverage industry standards). That is why "mainframes" outperform racks of x86 PCs. There really isn't anything magical about the hardware. The real magic is the fact that the software is written by guys who grew up understanding how to processes transactions in a couple K bytes of memory, and the machines grew, as the transaction load did. The result is code which understands the hardware and is crazy optimized in the critical paths. The fact that frequently the critical paths all fit in a fraction of a modern L1 cache doesn't hurt either.
More specifically to your link. While the details vary a bit, modern PC hardware doesn't conceptually differ that much from mainframes. You could just as well ask the same question of a modern PC... Sure you can open a file and treat it as a stream of records, but unless you make sure to size your records on a multiple of 4k (was 512 until recently, although RAID controllers complicate things, as does flash) you will have read/modify/write cycles rather than simple write cycles. Plus, depending on your access method, the kernel may get involved and bounce buffer everything rather than DMA'ing directly to/from the page storing the data. Yah sure, the track/sector meta data on a modern hard-drive varies a bit from the answer given, but you might find a modern SSD that compresses its read/write operations doing things far closer to what was described. So, given a machine with a couple K of memory. You need something that today we would consider the front-end (html/javascript), back-end business logic, database, OS, drivers and disk firmware all in a single piece of code. What would it look like? Yah, all those layers would collapse, and your database records would look a lot like the disk sectors...
For something even closer, you could consider the options to tar, and modern tape drives which continue to actually support the concept of fixed vs variable block reads/writes and blocking factors, and with recent encryption standards even allow what is effectively per block metadata.
My point is that while a lot of the terminology and things exposed on a daily basis with a mainframe seem strange to someone at first glance, a modern server has just as much (if not far more) strange behaviors buried it in. The difference frequently are the layers of standardized interfaces, protocols, and software stacks layered below what most people consider their "software stack".