This is a good question, I've been thinking about it and I can't really think of many reasons. Just my guesses but:
- It's free to play. The Battle Royal mode that is, not the actual full 'zombie' game that it was initially made as. So being F2P could help (probably does help a lot; I know it did for me otherwise I would have never tried or played it at all, ever).
- It looks like that "Battle Royal" types of games, or game modes, is a rather new trend in gaming. And in our day and age gaming trends spread out fast(er) with social media / streaming / Internet / word of mouth and so on. And since it's F2P there's a lot of people who just think "Well, let's just try it and we'll see...", that helps too.
- If I'm not mistaken, Fortnite has unique features for itself, mostly the 'crafting' part (and crafting on-the-fly... sometimes literally), but probably other things in direct comparison to other similar types of games. I wouldn't be aware of any other unique features it has compared to others though, I don't know enough about this type of games in general. But I'm fairly sure that Fortnite's "crafting" / building system is unique in this new Battle Royal gaming trend.
- It has a 'friendly', easy-on-the-eye art style, perhaps incites a wider range of gamers to give it a try (the visuals have a bit of a Team Fortress 2 vibe to them, and that's not a bad thing).
- There's a bit of humor, from dancing emotes to 'silly', "for the heck of it" character models that developers seem to just have fun with (and people have fun playing with). And there's a John Wick model (what's not to like?).
- It seems to be well optimized and runs smooth on max graphics (the non-photo realistic, approachable, "easy" art style probably helps a lot for that).
Now, I myself really didn't have any interest in that game at first glance. My cousin, however, tried it for a few weeks until just recently when he convinced me to at least try it (it's F2P so... indeed, it helps). I played it with him (never played it alone). Now I can say, that it can genuinely be fun sometimes, but it's very brief. You don't "have" to build any structures but it does help (mostly for giving yourself cover on the spot if you don't have any otherwise). However, for a guy whose getting older rather than younger I don't have the twitch reflexes I used to have in either FPS or 3rd person shooters. And I'm usually not too much of a fan when it comes to games that require quick thinking on the spot between too many things. So trying to bunny-hop Quake or Overwatch-style, craft a wall and/or stairs or a complete damn castle, while aiming for the head, while strafing, while switching weapons for the proper range or situation, while preparing for the enemy to show up from a window in a building or preparing for anything from around the corner, while checking for traps in a house while... while this... while that, while things. It's generally just not for me anymore. I mean... you REALLY have to like it (obviously). I just can't think of any good reasons to play it alone now that's for sure. In my opinion playing it with at least one friend is almost required (but that's just me, I had and still have the same opinion for some other games like Left 4 Dead and Vermintide for example).
But, I won't lie; I did have some very brief, fun moments. They are brief in general because overall Fortnite is ultimately no different than about 90% of all the modern shooters I've ever seen and played since something like mid 2000s. And that specifically is in reference to how you're made out of cardboard and things kill you too fast to have the time to react or to counter-attack; even with a 'shield' or armor or whatever power-ups or consumables you have (or wear) to reduce damage. So playing with my cousin helped a bit since we were two. Playing in a larger party must definitely change the whole dynamic of the game (for essentially having a LOT more chances to survive and, therefor, PLAY the damn game longer than 5 minutes). I did tell my cousin that it was my main issue, Fortnite in all its shiny (and probably very ephemeral) glory of the Battle Royal trend is really not that different from all the rest. You'll play longer if you're good, and you'll suffer and die quickly if you're the slightest of the casual players, no matter how much shield you got; unless you were lucky enough to find something like a rocket launcher at the beginning and most people avoid you (until they find a sniper rifle or a grenade launcher for themselves of course).
But, with this said, I don't "hate" the game. I do understand why right now it's popular. It's "the cool game" to play and I've been there too, I've done that when I was younger so I'm not one to speak against anyone out there who enjoys the game for what it is, or because "It's the popular thing to play" at the moment (believe me, when it comes to trends, I used to eat them for breakfast and demanded even more back in the days). I had some laughs when I played a few games with my cousin, we did have some fun here and there (that I want to underling again, because the game does have its moments). However, the two main things I do like about it, is that 1) When you die, you don't have to keep watching the match in spectator mode (you can, if you want to), so you don't lose too much time after death (specially if you die within the first 2 or 3 minutes after you land); just quit the match and find another one almost immediately after, so for that aspect it's well made. And 2) The very Battle Royal game mode, gameplay mechanic / concept in general (open map, then survive to the last lone player, or last team; while said map progressively becomes smaller to avoid camping, increasing tension over time, etc) is not a bad thing really, it's enjoyable to some extent. And well I said two things but... I'll also add 3) I like that the game is made in such a way as to not take itself too seriously, there's some silliness thrown in with models and emotes, it's light-hearted and can be enjoyed by a large audience and age groups.
So, the gist of it? Ultimately, I think that Fortnite specifically works well right now because the momentum is very good (within the period of time while this trend is still alive and active), and it coincides with free accessibility (obviously, with optional micro transactions).