The continue item being a coin makes sense when you consider that the game is set in an arcade machine.
In a similar vein, much of the game's infamously unfair difficulty is due to the game coming alive and literally trying to kill you.
Heck, even the game's length can be attributed to this. Bear in mind that, in-universe, the game's a walk-in virtual reality machine, so every level you go through would physically exhaust the player character, what with all the running, jumping, and swinging you'll be doing. The Final Boss wants to be good and sure you're at the end of your rope when you finally encounter him.
Casey's name is a homonym of the initials for "Kid Chameleon."
