It's a Battle Royal, basically a big map that shrinks over time and if you are outside the "play area" you receive damage until you get inside again or you die.
Pubg wasn't the first. The crown for that is for H1Z1 or Z1 battle royale as it's known these days. It was a dayZ clone with a stand alone battle royale version.
Even H1Z1 wasn't the first if you include mods for Arma, minecraft, DayZ and probably more.
Pubg standalone may not have been first, but in its mod form for arma i think it was the first. Someone less lazy can probably look up the specific dates