The point of the parent comment is that this is not a property of numbers in general. It's just a coincidence that only works in base-10.
For example, a prime number is prime in every base. An irrational number is irrational in every base. Collatz conjecture is valid in every base. This one is not.
What? Not at all. In fact, trying it in other bases, as well as with other numbers of digits (in both base 10 and other bases), is a useful way to get some insights into why it happens.
So, yes, the described "special" thing about 6174 is actually a special thing about the string 6174 (representing a number in base-10). And I'd say the fact so many people in this very thread don't understand it is exactly the proof that the GPs comment actually has some merit. People kinda mix up properties of numbers and properties of some other mathematical objects — like their representations in base-10. Most of numerological games are concerned with the latter. Which is why it's especially interesting, when something like that happens to hold in other bases, which sadly just isn't the case with Kaprekar's constant.
Here are some additional examples:
dec, 3 digits: 495
hex, 3 digits: 7F8
hex, 30 digits: EECCAA88664421FFDDBB9977553312
dec, 30 digits: 988766544332209987766554332111
hex, 100 digits: FFFFEEEEDDCCCCBBAAAA9998888776666554444333222210FFFFEEDDDDCCCBBBBAA999988777766655554433332211110001
dec, 100 digits: 9999998888888877666666665544444444332222222210999999998877777777665555555544333333332211111111000001
Finally someone noticed the irony, thank you.
(On the other hand, at least some people also criticize my tone rather than the point I'm making, which I guess is fair as well.)
An argument against being overly pedantic in this case is that this is a neat and accessible example of something quirky about numbers, and so even people who don't know much about numbering systems can approach it. If you instead emphasize that it's base 10 or that there is "no such thing as a 4 digit number", the main thing you'll probably do is cause disinterest in anyone who is sometimes overwhelmed by math. :)
Randomly, one of my sons told me about 6174 just a week ago, and it turned into an interesting conversation following by a little programming to find more of these numbers. After we went down that rabbit hole for awhile, then the conversation shifted to how these numbers might look in e.g. hexadecimal, and that seemed about the right time for that topic to come up.