This argument has made this thread dumb.
Exclusive normally just means only on that company's systems. So any first party game would apply.
You can say exclusive and not ports of old games, so then MK8D wouldn't count.
And sure if you really wanna be technical about exclusive just to the system BotW wouldn't count, but Switch was the primary release for BotW, as it launched same day on a dead (and failed) system.
I get what Permalite is saying about exclusive to Switch, but most people consider BotW to be a Switch exclusive, and if we wanna use the term in it's normal sense then any old port first party game applies as well.
I'd say go ahead and use the normal usage of exclusive, meaning the games aren't on Xbox, Playstation, or PC. Cuz then there is no stupid debate about BotW, and you can throw in an obvious exlcusive like MK8D, and possibly other games like 3D World, or whatever Nintendo ports you happen to love that are available on the Switch.
Between cross gen titles, the mass production of old ports these days including remakes and remasters, backwards compatibility, and retro game services, talking about games that are only every released on a single system as exclusive kinda loses it's meaning because what is only available on a single system today could easily be on more systems in the future. If you still want a decently strict definition of exclusive then just stick to it must be launched as a new game on the system and isn't available on the other company's hardware - in this case BotW is an exclusive because it launched on Switch as a brand new never before seen game and is first party.