That whole tutorial is quite a hack job. The part about attaching a crystal to two wires to create a nasty "EMI generator" is particularly fishy; I would question if these people have the slightest clue about EMC.
As seen in other pictures in that same tutorial, the end result of the soldering specifically is not pretty and a lot of the joints are probably cold. This will by no means be reliable over time, especially not if the device is regularly exposed to moist air, which one has to assume will happen.
In order to do a proper solder joint, the two metal surfaces must touch with no space between them. It is really as simple as that - you can never do a proper joint by "bridging" two surfaces with solder.
With two PCB next to each other, that is never certain, because the space between the pads on the lower board and the holes on the top board is unknown. In the worst case the solder will only wet on the hole and then just touch the pad below by chance. Oxidation or shock/vibration will break that connection sooner or later.
In order to carry out this job with some manner of reliability, you will need a hot air soldering gun, solder paste, soak the whole thing in flux and then do x-ray inspection. Basically flux & (re)heat the part over and over at a professional assembly shop until you happen to get it right, which isn't ideal at all (and expensive).
Unfortunately the problem seems to be the PCB design, it ought to have a header strip on the bottom PCB and then you could solder the pins to the holes with more confidence and easier inspection. A suitable low-profile connector like maybe a "bottom entry" socket/header might have worked, or some manner of "mezzanine" connector.