First, that's not what he does. What he does is curl his fingers in anger and say "
I realize a simple child like you knows nothing of magic, but spells like this take time and a steady hand! Can’t you wait quietly like a good boy? Hmm? You petulant brat…" He's still being condescending and he clearly still retains his composure. He's annoyed, sure, but just having an emotion is not an arc or a change in character.
He then dramatically stares at the floor and says "
You’ve pushed me too far. I’ve waited my whole existence for this! This is my moment! You know what? Fine! If you’re so intent on hurrying to your grave, I’ll be happy to show you the way! This time there will be no heroic escape. I was a fool to toy with you and let you walk away with your life before, but I won’t make that mistake again." He then does a Dragonball ki charge and turns into a porcelain doll. This is the angriest he gets, which is understandable, but we
still see his condescension, his self-assurance that he can destroy Link if he just stops playing with him.
After he lifts himself and Link into the air he drops the frown and the tense fingers and says "
If only I’d put you in your place from the very beginning [condescension].
Show a human a little mercy and next thing you know, he thinks himself your equal [condescension]
! Given my station, I had to maintain some semblance of dignity, so I let you run with your life… Twice, even [self-assurance].
Such a guilty pleasure… [condescension]
But instead of scurrying away like any creature with a basic instinct to survive, you just kept coming back. Again… and again… and again [condescension]"
Notice a clear pattern here? Ghirahim got angry for about twelve seconds and powered up so he could kill Link, but his attitude didn't change at all. His outlook didn't change. His motivations didn't change even, he still just wants Link to not interfere. The
only thing different between this scene and literally every other with Ghirahim is that this time he's going to kill Link because he recognises Link isn't going to be scared off. The fact it takes Ghirahim until the very end of the game to realise this is the perfect indicator that he's remained completely static for the whole story.
One last quote to drive this point home. The next thing Ghirahim says is "
For you, boy, I’ve prepared a most appropriate and humiliating death. I even have a pet name for it—I call it the endless plunge! First, I will take my time bludgeoning you, and when I grow bored of it, I will drive you to the edge and deliver a last strike and send you falling to your doom! I’ll delight in casting your body into this pit and snuffing out the flame of your life! Your broken body will serve as a fine sustenance for the demon king!"
So this guy who's 'totally lost his cool' is calmly explaining in detail what he's going to do to Link (which is a method slow and complex enough to show he's not enraged in the way you suggest) and he even states outright that he's going to take his time and wait until he's bored before he does the thing you seem to think he's so furiously intent on doing. Ghirahim doesn't lose his cool, dude. He gets annoyed for a moment and then he's right back to the way he has been the whole game. Even in the fight itself, it's the same slow-paced affair as his other fights, with Ghirahim telegraphing his attacks for four seconds before doing anything. If he really lost his cool he'd be aggressively pressing the attack constantly, trying to tear Link to shreds and forcing you onto the defensive. That doesn't happen because Ghirahim doesn't have any kind of arc.
Second, even if Ghirahim did completely lose his cool at the very end, that
still wouldn't be an arc, let alone an "excellent" one. Do you honestly think one single scene constitutes a character arc? That a character can remain fixed for the entire story only to suddenly be entirely different at the very end with no development towards that point? I don't have any disagreement with you on the general notion that seeing a character gradually lose everything until they're nothing but a desperate, near-feral mess lashing out in anger or fear or hatred can be interesting and engaging, but Ghirahim is absolutely not an example of this.