When messing with antennas, things like distance needs to be thoroughly calculated. Foil can help in many ways, but it can also make things worse—antenna calculations are tricky.
Done wrong this will increase reflected energy at the feed point and make the transceiver run hotter than it is supposed to, possibly leading to an early failure. Measuring SWR at 2.4/5 GHz requires some expensive instruments; note that the link you provided has only "calculated" SWR, not measured. Wifi doesn't involve much power, but these low cost Wifi transceivers are engineered with rather limited headroom for reflected energy and shipped with antennas that work within those limits, so if you do this you're a test pilot; there is no complaining if it lunches itself.
As long as you're not running a high-power transceiver (i.e. not consumer gear or consumer gear out of legal spec), I would not be worrying about SWR problems. Consumer Wi-Fi chipsets are designed to be fairly rugged. They normally operate nowhere near their limits.
Especially at high frequencies. One of the first things I did when I got access to a computer as a kid was to write an antenna calculation program for Yagi antennae.
Impressive gain by the way, a factor of 8 (almost 9 dB) from that super simple mod.
This particular example of yagi for wifi - what's the logic to customize it for my router ?
In short, I'm looking for logic to repeat this for my router's dipole antenna and possibly with custom wires (not #14 or paperclips of unknown thickness mentioned there)
As you already have a working dipole (which you have in this case), the primary thing to consider is the element lengths and spacings. If you don't have one of those routers with massive (and empty!) plastic antennas, there's probably a good chance that you can use the authors design parameters.
Otherwise, there's plenty of 3-element Yagi-Uda calculators online where you can stuff in various amounts of parameters and get the unknowns—the author used fancy antenna simulation software, but you don't need that.
When messing with antennas, things like distance needs to be thoroughly calculated. Foil can help in many ways, but it can also make things worse—antenna calculations are tricky.