Minecraft (hunger game mod) > DayZ/H1Z1 > PUBG > Fortnite
At each step, the genre grew by 1 or 2 orders or magnitude. So while Fortnite is by far the largest BR game now, if you look at the log-graph, they each had an almost equal impact on getting to where we are today and are an important part of the genre's history.
Edit: Oh I just looked it up. The mod was PUBG. I just realized it was the same guy who made it. It was released as a mod for Arma in 2015 by a player who went by the handle "PlayerUnknown". So I guess it was after the minecraft mod.
PUBG proved out the incredible appeal and potential of Battle Royale. Despite being a technical mess, it was a massive success and a game changer for the industry. It was the key catalyst and why Fortnite (and many others) added the mode.
This is not to take anything away from Fortnite though! They absolutely took it to the next level of awareness.
Minecraft had nothing to do with it. PU was inspired by the Battle Royale novel/movie and The Running Man. He forked the Day Z ARMA2 mod and made DayZ: Battle Royale, and that predates H1Z1 KotH by 3 years.
That's really downplaying the success of PUBG though. It was the #1 most watched game on Twitch before Fortnite overtook it. Sure, Fortnite is more popular now, but PUBG was literally the most popular game at the reveleant time.
I think the key word in that quote is popularized — even if earlier games did it, these are the two to demonstrate widespread appeal.