Here I will try to stick to both Socrates' and Dr Rick's rule about not being long winded: I don't think that Socrates "won" this argument. It doesn't feel to me like Plato is ripping the sophists a new one here. Indeed, Gorgias' students sort of sit back and admit that there is no talking to this guy Socrates, who seemed so very chill to start. Socrates is using a strategy that leaves no room for conversation, and is asking all these yes/no questions. He even tells people , "now don't dance around it; just tell me yes." Is that any way to have a conversation, a dialogue, an understanding? On page 843 was the last straw, and in my margins I keep scribbling, "NO NO NO NO! Stop agreeing!"
Socrates won't answer questions posed to him, he ignores the possibility that things are not clear cut, and in the end it all comes down to what happens in the after life, which is just not on the table for discussion. How is this philosophy? How is this truth? Who really ends up looking like a jerk in this dialogue: Socrates or Gorgias, who even stops his students at one point and tells them to play along with Socrates? Though I think the arguement about might making right was a little far fetched, there was little to do at that point. Socrates forced the baby sophists into a corner where they had to take the "opposite" side to have any chance at playing. The problem being that they stopped trying to define what action an orator is taking (something that is multidisiplinary... not evil Socrates) and started talking about the moral responsibility of a teacher (of anything: A carpenter can kill someone with shoddy work Socrates, but do you ask the master carpenter to teach morality? Do you!?), which wasn't on the table. What do you call and orator and what the hell do they do: that was the question. Come on!
If this dialogue was designed to make me hate the sophists it didn't work, at least not 2300 years later... But if I give Plato the benefit of the doubt I would say the argument he is making is more about the nature of argument then about the morality of the sophists.