No. A story is more than a sequence of decisions and events, and we can care about character without caring about story.
But hey, if anyone ever wonders why I get so cranky about "narrativism" and "story games", the attitude on display by the above poster, that self-serving attempt to claim anything remotely interesting about RPGs as part of "story", is a chunk of why.
Just because something is a useful tool or necessary element for your preferred type of RPG (or other game, some of these games leave the overlap area of the Venn diagram), that doesn't give your preferred type of RPG ownership of that element.
Just because YOU are deliberately crafting or telling a story when you game, that doesn't preclude others from playing without any storytelling at all -- including those who are deeply into character and setting.
And here we get into part of why I cringe at the notion of "archetypes" or "types of characters" in RPGs -- the inference some make that a certain character is selected for a certain type of story.
Because all this time, I've been selecting and building each character because I found the character interesting, not because of any desire to tell any stories of a certain type or not.
Meh.
I once took my character out of an entire arc of a campaign, like weeks worth of material, because it would have required her to violate multiple aspects of her code of honor. Luckily it was a game focused on a single city, so I could be around for some other things that were going on, but for those 4 or 5 sessions I was involved in less than an hour out of each 6+ hour session.
Unfortunately, too many people don't understand that, have no sense of scale or nuance or subtlety, and only recognize crippling flaws as legitimate, and think their character has to be either terminally stupid or "perfect" with no middle ground.