I'm to tired to get overly technical about why this is wrong but I'll try to get it out.
The point of this episode, along with Soul Purpose, Damage, and You're Welcome is part of a theme that is not about Spike being better then Angel, it's about Angel losing his sense of purpose.
The only reason why Spike beats Angel at this, is because as Angelus taught him so many years ago, you take what you want. Angel in his heart did not know what he wanted and Spike did.
Angel got Dru first, he got his soul first, he got Buffy first, he became a Champion first, he got his own 'scooby gang' first, he got his mission from the PTB first, if you want to get technical, Angelus was a more feared vampire then Spike. Angel has always beaten Spike in everything ever because Angel always had a purpose. This time he isn't sure what he's fighting for and if it's worth it, and Spikes combination of 'screw you Angel' and confidence in being a champion is just the edge he needs to finally notch a win against Big Brother.
So yes, not in any way about Spike being superior to Angel, on the contrary it's about Angel and what's going on inside him. Thanks to this and a few other events Angel regains his balance, finds his purpose, becomes the leader he has been in the past and by the time Not Fade Away rolls around, Spike has acknowledged Angel as the leader.
Yeah the Cup thing is a total reference to the Holy Grail. The funny part being that the cup was a complete and utter fabrication. Angel and Spike were total rubes and fell for the grandeur of the story heh. Why the heck would someone keep a random cup in the middle of an abandoned opera house in the Nevada desert that just so happened to have the ability to choose the worlds champion? Seems odd, someone should have asked some questions.
That post was awesome! I agree with how you put it for Spike winning over Angel there. He was not sure of anything at that point and Spike was(at least more than Angel).