quake, unreal tournament, tribes, battlefield, planetside.. Deathmatch with many players. Same thing pretty much, but with more action.
That's exactly why we play BR games.
These days I play mostly PUBG. Before that, Day of Infamy. Before that, Insurgency. Notice a trend? Each one of those games has a lot at stake (relatively speaking) when you get into an engagement. If you die, you sit out for a while. They're about communication and coordination between players on the same team.
PUBG (and Fortnite, though that's not my preference) take it to a whole other level. It's not uncommon for me to play a game of PUBG where the first 10-15 minutes is spent either not encountering anyone or spotting them before they spot me and purposefully avoiding them. It's about tactics - either coordination with your squad, or maneuvering into a better position for the next phase of the game, or waiting until someone you're stalking has engaged someone else before engaging them.
Because the preparation is longer, there's more at risk when you actually engage, and the anticipation builds to a crescendo. So, yeah - there may only be seconds of "action" in a PUBG match, but that's the whole point.
This is Fortnite build battling. BR as a whole just refers to a game ruleset that forces and encourages a last-man-standing situation. That part has been done before there was a video game. But the details of what's being communicated are different. They're different even between Rust and PUBG, despite both of them being military styled. Fortnite is in a class of its own since it's cartoonish and the building and mobility options present a lot of unique options. Even comparisons to Minecraft don't fit since the build system is different.
Performing jadedness about the games being "done before" is basically like saying new movies are just collections of old cliches. Even when they are, they end up saying something different.
I'll just keep playing Quake (actually I'm mainly playing puzzles and graphic novels right now) until people get tired of Battle Royale modes and need a break from them.
As an aside, I loved Tribes 2 construction mod.
Battle royale was available, long before battle royale was cool.
There were also a lot of other gameplay available on top of death match, all built in: team death match, assault, onslaught, capture the flags, domination, etc...
If you look at good players who win their games, it's a lot about being at the right place at the right time. Get the best stuff and locations for yourself and don't let opponents have anything.
Sorry, but you're talking about something completely different.
It seems like what you're describing is definitely the mainstream take on the genre right now, but I think you could make another variant that isn't like the popular ones today but is still a BR.