Edit: By cheap I mean something like in the article or a bit more expensive, for sure < $1000. By CPU I mean something like an M1. By GPU I mean something like an Nvidia 2080Ti.
In retrocomputing for example they're useful for building accelerators that bolt much faster CPU's of a different model (like 68060 accelerators for an Amiga) or implementing a new graphics card with HD resolution, HDMI, and SDRAM controllers like the ZZ9000 https://shop.mntre.com/products/zz9000-for-amiga-preorder
Less than a microsecond of latency without even trying and 100% predictability.
If needed, you can place more processes on the chip, all running in parallel with zero interference between them.
FPGAs give you the ability to process a lot of data in parallel, with very low latency. As soon as you make use of this, a CPU has a very hard time to compete. If you have e.g. radio data from an SDR, you might want to process it on an FPGA → if you look at various SDR modules, you'll find an onboard FPGA to do exactly that. If you want to process video signals with low latency and with low power consumption, again, you might want to do it on an FPGA → look at video interface cards from BlackMagic Design and most of them will have an FPGA on board. If you have complex mathematical models to emulate e.g. some vintage analog audio hardware, which would create some serious CPU load on a PC, you might want to do it on an FPGA instead → this is what some companies like e.g. UAD do with FPGA based accelerators. If you have high-speed interfaces, like e.g. in a network router/switch, you might want to implement the packet processing in an FPGA → this is what some network equipment does, unless it uses an ASIC. There are countless applications for FPGAs.
Sometimes FPGAs are also the prototype "playground" where you can validate your design before you build an ASIC.
And finally, many FPGAs aren't really that expensive, at least if you ignore the crazy price increase from 2020+. The FPGA alone from the Basys-3 development board from the article (an XC7A35T) costs something around $20-25, at least if you don't need the exact same package. Of course that's only the FPGA and you still might want to add some external configuration flash, RAM and connectivity, but that's still very cheap. To give you an idea, a 256MB DDR3 RAM chip costs maybe $3-5. If you want to connect this to your computer, you could use PCIe, which is directly supported by these Artix-7 FPGAs. Of course there are much bigger and more expensive FPGAs available, but I think you can imagine already that you can do a lot with a $1000 hardware budget.
https://www.digikey.de/de/products/detail/lattice-semiconduc...
This price is ridiculous. I also know you can get 640 Lists for slightly more but I can't find the link.
Since they are just general digital logic machines they can be obviously implement a cpu and are great are parallel computation, but in most cases cpus and gpus are much better at general computation because they’re specifically designed for that task.