What exactly makes the duo so powerful? Their strengths complement each other very well: Shiro, a reincarnation of a literal Robot Girl, can perfectly play by the rules no matter how complicated they are, while Sora, representing intuition and ingenuity, is able to adjust to changing circumstances and improvise a plan on the spot. This is very similar to how computers and humans, in tandem, can achieve better results than either of them alone, whether in board games or other more pragmatic pursuits. The duo's aspiration to become a literal god is nothing but The Singularity in human form.
Shiro and Sora generally suffer nervous breakdowns when apart from each other, so why did Shiro not suffer it when Sora was not present during Episode 8's and 9's Retgone situation? Because he was still there in a way except immaterial - she hears his voice and constantly feels that there is something else which was in fact Sora who followed her around while trying to get her to realize what really happened.
Furthermore, how they were able to be separated while playing the game in episode 10 and 11. They were holding hands in the real world; they don't care about the setting of the game world once they learn it's just a simulation.
Jibril's devotion towards Sora (and Shiro by extension) is not only because she bet herself and lost, but also because they're challenging Tet, an Old Deus. Challenging someone to a game is practically a war declaration in Disboard, so 『 』's intention of defeating Tet is the closest equivalent to killing an Old Deus you can get now that bloodshed is forbidden. Jibril has finally found a master who would allow her to be the god-killing Living Weapon she was meant to be.
It seems weird that Imanity's race piece is the white king; but if you think further, it actually makes sense. The king piece is the weakest piece as it can only move one square per turn, but it's also the most important and the whole point in Chess is taking over the opponent's king. Imanity is the weakest Exceed but thanks to Sora's and Shiro's arrival, Imanity is slowly becoming the axis of the whole chessboard that is Disboard.
It can also be Foreshadowing: if Imanity is the weak but indispensable king, it means that all the others 15 pieces are at it's disposition to serve and protect; Imanity will indeed take over the world and the other 15 Exceeds will be supporting them against Tet.
Tet possesing the black king piece actually says more than just being the One True God, opposing Sora and Shiro. Tet was the weakest of the Old Dei, but his survival earned him godhood.
The colours themselves are symbolic: the white player goes first (but supposedly black wins). So it makes sense that the 16 Exceeds are the white side and go for the attack, while Tet with his black pieces will defend but, presumably, win (he's the God of Games, after all, so there's no way he'd want to lose the ultimate game of chess).
Sora's coronation speech is right on the money. As the series progress, we see that although the other races now also rely on planning and knowledge, the backbone of their way of doing things, as well their trump cards, are still their physical and magical abilities. Whether it's magic cheating, or extreme physical endurance and knowledge gained through long life, or physics-defying martial abilities, the other races use their brains to supplement their brawns. Now they are being defeated by a pair of no-brawn siblings that rely completely on their brains.
Shiro's distant personality is easy to explain as a child who can't fit in and is bullied for her genius. But what about Sora? How can someone who is a NEET and Hikikomori have so much charisma? It's the same reason Sora often acts like a Sociopathic Hero. When he's displaying his charisma, he's lying through his teeth and treating the entire thing as a game. All he's doing is answering what the NPCs want to hear so he can progress in the game. He is offering nothing, factual or emotional, on the line. He has so much confidence when he talks because he is risking nothing while getting ahead. This also played a role in why he became a Hikikomori.
Sora and Shiro's reactions to being separated from each other mirror Riku and Shuvi's thoughts before their deaths.
Shiro locks up and goes catatonic. During Shuvi's ultimately futile battle against Jibril, she laments that it happened because she strayed from Riku's side.
Sora's cocky attitude breaks down and he starts apologizing profusely. In Riku's last moments, he lamented that without Shuvi acting as his Morality Pet, he sent the entire Ex-Machina race to their deaths and thus believed himself unworthy of becoming the One True God of Disboard.
Sora and Shiro's apperances. They're practically Riku and Shuvi but with their hair and eye colors switched. Sora and Shiro are how Riku and Shuvi imagined their hypothetical children would look like.
The consequences of Imanity losing their Race Piece and no longer being protected by the Ten Pledges are bad enough, but imagine what would happen to the human slaves of Elven Gard if their masters no longer have to obey the prohibition against violence. With this in mind, it's no surprise that Kurami and Feel felt the need to take action.
The series runs on the prospect that Shiro and Sora will unite the 16 Exceeds, collect all chess pieces and then challenge Tet to the ultimate game. But what happens if, after all the trouble they went through, they'd actually lose? In the case of the game, nothing less than risking those same race pieces would be appropriate when challenging God himself. A subsequent loss could easily mean the same as when Imanity risked its Race Piece, except this time all Exceeds would fall out of the protection clauses. A repeat of the bloody war from times long past would loom again on the horizon once certain forces realize they no longer have to behave. Tet would have unwittingly doomed his whole world and he couldn't go back on it if those were the conditions, either.