The other part is the weapons. Think of all the heroes, in any (fiction) genre, in any medium. Most of these heroes will have items attached to them - usually one or two. Whether it is a lightsaber, Anduril, or even a pen or a voice, they have one main tool associated with them. Even video game heroes such as those mentioned in the article, like Link or Master Chief, usually have their primary, identifying weapon, and sometimes armor or other secondary item, even though oftentimes it isn't really the main or even the most common weapon you use in the game.
More games need these. Specifically, more games need these to truly be the defining weapon, and have differing uses for the one weapon instead of relying on huge inventories to provide interesting gameplay. Surprisingly, many RPGs manage not to do this, despite the fact that they are the ones that really should the best. They don't even have one at all, most of the time, instead letting you choose your own - but then they don't capitalize on it. These weapons, instead of becoming your own Excalibur, become "Uber Sword of Awesome", with no personality, no story, and no individuality, identical to thousands or millions of others across the world. The main thing they need, even if you choose it yourself, is permanence, a name, and a distinctive style of some sort.
P.S: My favorite example of a truly defining weapon, both in the minds of the fans and in the canon of the game itself: the Keyblades.
