I wouldn't call Cave Story an RPG or a shooter at all. I can't really think of many role-playing game elements it has- there are no stats or anything, and the only leveling is the weapon system, but even that is reversible. It shares a focus on plot with RPGs, but plot an RPG does not make. I don't know how it can be called a shooter at all, except in that the protagonist uses various projectile weapons. It isn't a first- or third-person shooter, or a top-down shooter. Cave Story is as much a shooter as Super Mario World is when Mario has a fire flower. Cave Story is an action-adventure/platformer.
Anyway. Cave Story is a good game. It's probably the most influential independent video game yet made. I like the gameplay, but I found the plot hanging together very loosely, and I really hate the improbable things you must do in order to access the "good" ending. And the irrational decision one must make to later get the best weapon (a decision never hinted at). And the extremely irrational decision one must make in order to get an upgraded version of an otherwise unupgraded item late in the game.