Generally speaking "kids" covers anybody under the age of about 18 so yes sexually developed kids are included. Remember that puberty starts around 11 years old.

Gender incongruence also doesn't fully rely on sexual characteristics alone. An aspect of gender is that it is inate. Trans children are often confused by what they are told if they try and self identity and are told that they are not that gender by adults who represent an authority. It is actually very easy to essentially gaslight your child into self identiting as their birth sex if they are kept in situations where don't know there are other options... But just because they don't know being trans is a thing doesn't mean that they aren't trans or struggle with being trans. It just means they do so in isolation where they don't have words. When I was growing up that was the case.

After a certain point a lot of the social siloing process puts you in a social category where you are segregated. For a lot of people this is fine. The silo puts them with other people who don't mind being siloed. A lot of cis people don't seem like they are comfortably cis because they have a gender identity that solidly matches their sex... It's like they have a nebulous gender identity where they don't really care. Whatever program they are given is fine so they have real issues understanding having a strong fixed gender identity at all. When someone with no real preference is told their social category is tied to their sex they have no reason to question treating the two as linked facts. If a cis person has a strong sense of gender identity and it matches then that's great! They experience gender euphoria, actually joy from expressing and being that matchup. They can also better relate to a mismatch.

Trans people however have an intenal sense of what they are and also what they are not that doesn't easy match with this concept of linked social and physical category. Other people of your birth sex never register to your brain fully as being "like you" so when people of your birth sex whose gender aligns or at least doesn't chafe are your only social bonding options you just feel alone, oddly alien and like there isn't really a solution for those things.

Being trans means trying to fit in with your birth sex makes just makes you feel more fake. You very quickly understand that there is a host of expectations about who you are, who it's normal to be friends with, what things you like and what activities you get to participate in based on your genitals. I grew up with generally depressed, socially anxious and feeling invisible as being my baseline normal because nothing I was handed or expected to do along this category resonated... so I was rejected by everyone for essentially never being comfortable. Trying to fake being comfortable so you aren't alone doesn't ultimately make you feel less alone.

All this before puberty. Once puberty hits the shit really hits the fan because people at the same time your body is changing in a very body horroresque way start treating you in ways where your sex is highlighted and comes with a whole host of new social gendered expectations. Everyone treats it all as a difficult rite of passage for everyone but at the same time you can see in real time that your struggle and a cis person's struggle are very different.