(Burning Wheel and games with a similarly inclined system)
(title is a bit of a hyperbole, for the sake of debate)
(also, spoilers if you haven't yet read the books/seen the first season)
Ned is played by Sean. Before the game, Sean writes down a Belief: "Honor above all."
Over the next eight sessions, the GM hammers on Sean's Belief. He puts Ned in situations where his honor comes into play, where it's put to question, where he has to make hard decisions in regards to it. He has NPC|Robert tell PC|Ned that they have to kill a pregnant girl. Ned says "No, it's not honorable." Ding, artha. The GM has NPC|Renly run up to PC|Ned and suggest a revolt. It's a sensible suggestion, all things considered, but it wouldn't be honorable. Ned says no. Ding, artha.
Sean hammers on his Belief as well. Once he learns the truth about the Queen's children, he decides. "I arrange a meeting with her," he says: "and when she's there I tell her I know. Because it's the honorable thing to do." Ding, artha.
All the while, we're all going "Fuuuuu-, Ned, don't do that!" and "Oh fuck, he didn't!" but between the lines (or not) we're also saying "That's good shit, Sean. That's good shit, GM.". It's good stuff!
Now, for eight sessions, Ned has been hitting on his belief, hard. Honor is clearly a big deal to this guy, it's an important part of the game. Yet another untenable situation is set up, a bang. Ned is offered a choice: Swallow up your honor and admit to treason or die. He cannot not make a choice.
We all know by now that this guy will gladly die for honor, nothing will move him. But then Varys reminds us: what about your daughters, lord Stark? Will you do it for your daughters? We're at the edge of our seats, which way will the story swing? And Sean picks: Ned admits to treason.
It's a big deal. It's a reversal for the character, a culmination of a Belief arc. Not only do we feel that the narrative space has changed, Sean/Ned also gets rewarded in artha for going against his Belief. Most importantly, the way the system is set up, a statement has been made. The Belief posed an implicit questions: What is honor worth? We got an answer: your children are more important than honor. That is a line that Ned won't cross. Again: Big Deal.
But then Joffrey says cut off his head anyway. Now, when the GM makes that decision, not only does he invalidate Sean's artha reward, not only does he totally negate the drama of Ned going against his belief, he also steamrolls the thematic statement that emerged from player-system interaction (a theme that emerged precisely because of the way the system is set up) and replaces it with some arbitrary one of his own. The whole big dramatic thematic question ("honor or death") was just turned into bullshit. Teh suck.
There are a few comments/flipsides/counterarguments to this.
One: It's possible that Ned was never a protagonist. I think I've argued in favor of this before, long before the TV series came out. The whole thing where Ned is set up as an important character (a lead character) is just smoke and mirrors bullshit. As a reader and a viewer you get played into believing that Ned is a PC, so it pays up later in shock value.
Two: I exaggerated in my title. The way it could have worked in BW (in theory) would be with the whole scene on the steps of the Sept of Baelor being a Duel of Wits. It's an argument conflict, with what's at stake Joffrey conceding that Ned should live and be sent to the wall. You script actions and roll for it. Ned admits his crimes, he even has Pycelle jump in with some helping dice and stuff. But he rolls terribly, loses the DoW, Joffrey doesn't have to agree, has him executed. The difference here is that (a) in the game Joffrey's decision wouldn't be surprising, because we'd see the dice and (b) Ned would probably have a shitton of artha and other means of leveling the playing field. Such a disastrous result would have been nigh impossible.
Three: This isn't to say that Ned's death sucks by default or that it isn't possible to do in games in general, it's just that BW and GoT actually fit different narrative aims, despite possible similarities. They are barking up different trees. Playing in different fields.
Four: Consider this old post by Vincent in which he outlines a kind of game where the dice decide "what kind of movie we're playing", metaphorically speaking. That is, the fact that Ned is a protagonist or not, lives or not, is a good guy or not is all up for grabs. It's only through playing that we find these things out. This ties right back into the Ned is "Not a Protagonist Character" (NPC) argument.
Five: Let me also remind you of the old-school paradigm where all characters are squishy and weak and if someone actually makes it to lvl 2, it's because they had to fight for it. It's not assumed that your character will live, it's not assumed that he's a hero, you have to earn it, through skill and luck. If he dies, then he never was a hero, just some schmuck who went down a dungeon and you roll up a new dude.