Playing X? I'll Show You Something Interesting - The Two Types of Indie Game

Clearly a cave story

Ok, I think I understand. Based on the games given as examples, the definition of each category would probably be:

An Earthbound Game: A game that focuses more on story depth than gameplay depth, their primary goal is to get you to emotionally feel something.

A Cave Story Game: A game that focuses more on gameplay depth than story depth, their primary goal is to challenge you with something.

Of course, there can be an Earthbound Game with challenges that are fun to master, or a Cave Story Game with emotional storytelling, but these tags simply state what their goal is as a game.