PUBG inspired nothing, those kind of battle royale games have been around for ages (ages in game terms, a year or two ago H1Z1 accidentally popularized battle royale as an alternate mode in its zombie survival game, which was in beta).
AFAIK PUBG was made in response to other games that used to be popular in the genre failing after major changes, specifically H1Z1.
EDIT: Fair-cop to them though, they've obviously done a greaat job. It's just that games like this are already coming out constantly, it's the new genre to clone. Before battle royale was that hot genre, it was MOBAs[1] + survival games a few years ago and MMOs were a few years before that. Battle Royale is actually a sort of spin off out of the survival genre. Another interesting thing to note is that survival/battle royale games have a lot of indie entrants who tend to have long alpha phases where hype makes them incredibly popular (DayZ, 7 days to die, Rust, Ark: Survial Evolved, Unturned, Don't Starve). Then the player base can sometimes die off as the game suffers from poor performance and slow development.
At the moment PUBG is suffering from lots of hackers, so we'll see whether it actually stays popular.
[1] Multiplayer online battle arena (5v5, top down, team game), spawned from a mod made for warcraft 3, popular examples include league of legends, DOTA2, Heroes of the Storm, etc.