Wow, so many possibilities, I'm going to go the Legend of Zelda, taking breath of the wild's map into account.
I would certainly love to run around battling other people with swords, bows, and bombs in order to become the best hero of Hyrule. Food would be used to restore health just like in breath of wild.
There could be a possibility to "hack" with magic the ancient machines to attack your opponents and also lure some enemies into them.
There could be a lot of customization in the form of clothing, armor, and boots. You could also incorporate Zelda: Majora's masks type of items where for a limited amount of time you can transform into a Zora, Goron, Deku or have faster speed with the bunny hood, the possibilities here are almost unlimited.
Certain skins would be available so can your character be a wide variety of Nintendo favorites. This can also work with existing and new amibos introducing new items, or new skins into the game.
You could also link the game to a Nintendo DS and have a portable version too. There is a lot that can be achieved with the Nintendo brand since it spans a lot of franchises and two systems that could interact to bring you a unique and great experience in a battle royale game.
Think it would work? I think Nintendo should do it NOW!
Runner-up