So, is there some kind of rule? Or is simply their inner OCD and these numbers are some kind of key numbers in music?
You're kind of on the right track. I think it may have been said before, but the thing with EDM music is, repetition is key, but not for repetition's sake.
One of the more conventional things about pop music that carries over to (most, not all) EDM music is common time. Common time is defined as 4 beats in a measure. The number 4 here is then key for this.
Since EDM features the number 4 here a lot, that usually means musical phrases are likely in a multiple of 4. To explain a phrase, it's essentially a group of measures that "speak" completely. So, if a phrase is in multiples of 4, it can take 4, 8, 16, etc. measures for a phrase.
It's hard to think that in EDM music is in phrases, because oftentimes, the space at the intro of the track is filled with mostly a beat loop and sound effects, and maybe some introductory bass line that repeats over and over. However, the feel that pushes the music onward is this division of phrasing. You'll notice in these longer intros, new elements get introduced every new phrase. What might start with just a kick drum and some hi-hats may be joined by a snare or clap a phrase later, and then a bass line a phrase later, etc.
As far as how long it takes to "complete" an intro, it's relative. The length is usually destined by the bpm against the length of the phrase. A phrase consisting of 4 measures of 4 beats each, at a tempo (read, speed) of 120bpm (meaning, 2 beats a second) is 8 seconds. A phrase of 8 measures like this is 16 seconds, etc.
As far as history, there are two things here. One is what tempos were used for EDM. Modern EDM derives from a variety of styles of electronic music, but the general setting in many sequencers was 120bpm. It is always adjustable, and in the case of EDM, it's mostly around 120bpm-130bpm. Other styles closely related, such as Trance, ues higher bpms, as low as 128bpm to about as high as 156bpm. But, intros last as long as they do because they are buffer for a DJ to mix seamlessly from one track to the next. As the bpm of a track can be altered by how fast a vinyl is spinning, it is the necessary time for a DJ to find a suitable revolution speed on the table, adjust the vinyl until one track meshes well into the next, and align the phrasing between the two tracks, before panning the volume from one turntable to the next. This time is meant to link the outro of one track to the intro of another track, essentially making it so that the music doesn't stop and flows well.