I have so many thoughts about this scene, and I finally managed to make the gifs to go with it, so here we go:
We know Arthur's going into the fight with the intention of letting Uther win so that the king can save face. But Uther makes this as hard as possible for Arthur, goading him and triggering him by saying stuff like "when I was your age I conquered camelot. I didn't inherit this kingdom, I won it" or "one day you'll be strong enough to take my crown, but not yet". And so as a consequence, at the beginning, Arthur fights him properly, with all the skill he has, letting Uther feel his anger. He quickly and efficiently overpowers Uther, throwing him to the ground.
But then, seeing Uther getting back up, desperate with fear of humiliation and almost hatred towards his son, Arthur's perception of Uther shifts. For maybe the first time in his life, Arthur sees his father for what he has become.
He sees the man he has looked up to all his life, the man he's always wanted to make proud more than anyone, the man who he always thought saw him as a disappointment. That man is now desperate, red in the face, lashing out like a panicked animal. And in this split second he turns from someone to be feared and admired to someone to be pitied. He is no threat to Arthur, he is no match for Arthur, and in this one moment Uther ceases to have power over Arthur.
So Arthur throws the fight, but even though the crowds cheer for Uther in the end, it is Arthur who has won. Uther may hold the sword to Arthur's chest, but they both know who is the stronger warrior, the better person out of the two. Arthur no longer needs his father's validation, because he has stopped looking up to him, has stopped fearing him, and instead feels only pity for his vain, desperate father who needs his own son others to feel small in order to feel powerful himself. The power dynamic between them has shifted and Arthur has defeated Uther more definitively than by the sword.
And Arthur doesn't feel pride or satisfaction at this realization, but a weird kind of sadness to see his childhood hero reduced to this, to see his father so desperate for the crowd's validation. Arthur can swallow his pride for the sake of his father (and you can see how hard it is for him) but Uther can't do the same for his son. It's in this exact moment that Arthur proves that he is truly ready to be king, that he is going to be a better king than Uther could ever dream of being.
Arthur and Uther fight | 3.11 "The Sorcerer's Shadow"