Arcadey to me means hard as fuck or cheap as fuck difficulty combined with being a graphical spectacle at the time. Arcade games aren't fair or balanced experiences, they needed to make money off these machines.
Mario Kart, F-Zero, and Smash are arcadey. Mario Kart is designed around skill and a ton of luck, it also got its own arcade cab. F-Zero GX, the last F-Zero entry, is tough as old man ballskin, it also got its own arcade cab. Smash is a unique fighter with a ton of execution required for high level play. They all fit an arcade mold.
Everything else isn't. 2D Mario isn't arcadey. An example of an arcade platformer would be Ghouls and Goblins, and 2D Mario, even the real Super Mario Bros 2, was never that unforgiving or tough. This would also apply to every 2D platformer that isn't Mario. 3D platforming collectatons aren't arcadey at all.
Metroid has always been an action adventure series.
Zelda has always been an action adventure series.
