I'm just saying that Paper Mario games tailor more elements towards the development of their stories than towards their inset gameplay. Partners have names and affected dialogue and particular appearances/outfits. None of that is there for the gameplay. When the game is sad, the music is sad; when a fight looks to be difficult, the music ramps up. That doesn't have anything to do with gameplay either. When you go to a new area, you get a "Chapter X" message. That's a reinforcement of the story. When you finish a chapter, the NPCs in the world and the messages of the world reflect that achievement, usually focusing as much or more on how it effects the plot or a set of characters than on what you actually did.
If you're saying its taken x amount of posts for me to "prove it," perhaps it simply can't be proven. It's meant to be subtle. The games are good because they don't seem story-centric, even if they are, or gameplay-centric, or art design centric, or anything. They feel like a whole, finished product with no glaringly obtuse or acute elements. Nintendo has made a large amount of games like that.
And still, if you look at what makes up Paper Mario as a game—gameplay, art design, music, sound effects, dialogue, narrative, tutortials, puzzles, items, "key" items—I think you'll find that as much or more of those elements are based on the plot, sub-plots and overall storytelling aspect as they are on just pure button-pushing gameplay. That is what makes it story-centric.