What is it about this game that has stuck with children? There have been free to play shooters before, and none have blown up with kids like this.
I'm struggling to name one that was playable on PS4 and Xbone in addition to PC before Fortnite existed. Quality F2P games have been a lot less common on Console up until very recently. It was the first BR game to come out on consoles, and at the time it was released a ton of people were really fed up with Bluehole's terrible support of PUBG and were interested in alternatives. On top that the game's art style and frequency of updates didn't hurt either. The combination of being F2P, great to play with friends, being decently generous to people with small amounts of money, (such as kids with allowances) having an appealing art style, and eventually having cross-platform play combined with getting to the market way before any real competition arrived was sort of a perfect storm that lead to it being as successful as it was. Epic's marketing and their means of keeping players engaged (such as the battlepass) have also been really good.
If you're reading carefully, you'll notice I didn't really mention anything about the gameplay there, and that's because aside from it possessing qualities that literally every other BR game has I feel like Fortnite's gameplay has been irrelevant to its success. I've played a fair amount of BRs, and while it's far from the worst I've played, I can name at least 4 that have better core gameplay than Fortnite. I think a massive chunk of people play Fortnite because it's a F2P BR that's playable on console that all their friends are also playing, not because the gameplay is just that good.