I was just wondering about this as it caught my eye while I was re-reading the Way of Kings.
Just some introductory remarks from what I gathered from Szeth's punishment; he has to do what his masters command of him to the letter.
When the thugs assault/kill the transient worker
Anyways twice during the book Szeth repeats the instructions that the Parshendi gave him on for the night that he killed King Gavilar
Instructions from the Prologue
Instruction from Interlude #3 - these ones appear in italics
The part that caught my attention is in bold. "but be seen doing it" I thought it strange that Szeth killed King Gavilar but did not kill in the way the Parshendi intended, he wasn't actually seen killing the king, he was alone when he did that. This could also imply just too be seen assaulting the kings chamber, and Szeth actually followed the instructions, but I think the Parshendi intended for anyone, but someone to witness that Szeth stick a Shardblade into Gavilar.
Also after catching that I went searching for the instructions from the Interlude #3 and apart from noting that they are different, the second instructions, they don't actually instruct Szeth to kill the King, just to get to him, not to kill the King... at least explicitly.
Anyways some extrapolation from all this
I'm assuming the Parshendi are not the "bad guys"....
The parshendi's decision to send Szeth was a decision in two parts
1. To test the King of the Alethi, his strength, honour all that... Since he was reading the "Way of Kings" he might have had some "Knights Radiant" abilities... and Szeth could potentially test or bring them out.. this lead to the second point
2. Szeth was sent to the to assassinate King Gavilar, but I think the Parshendi intended him to die in the attempt, put him out of his misery... his punishment etc.
Assuming these two points are true it would also explain why the Parshendi threw away his oathstone... Why would the Parshendi keep a servant that did not followed there instructions... that kept his honour?
From reading the Prologue he seemed to kill Gavilar more out of anger after Gavilar severely injured him, and there was all this pain. Basically Survival instinct.
Just thought it was strange, and wanted to put it out there.