He repurposed an old Arduino into an SPI flasher and a chip clip to sit on the bios flash chip.
The current exploit only runs far later, after the validation is performed. So unless you manage to mangle the code execution flow of the authentic firmware to the point that it skips the whitelists, you can't get rid of it.
EDIT: The obvious answer would be that they didn't have one handy and were competent enough that de- and re-soldering the chip was not a big deal.
EDIT (again): Also, they wanted to flash a NEW chip with the contents of the original so that they could fall back to the original in the event of failure.
[0] https://www.bios-mods.com/forum/Thread-TUTORIAL-Lenovo-X230-...
[1] https://www.digikey.com/product-detail/en/pomona-electronics...
Because they tried and it didn't work (third post). It seems to depend on the mobo as well as the programmer you're using, but sometimes SPI programming without removing the chip doesn't work, which has to do with the mobo consuming the power you're supplying to the chip. Some people work around that by supplying separate power but even then it's a crapshot.