Nephew to the King

This is one Lucianus, nephew to the king. (III,ii,230)

The parallel between the murder of Gonzago by Lucianus in the embedded play and the murder of Hamlet's father by Claudius is somewhat distorted by the fact that Lucianus is the King's nephew, not his brother. Aware of this discrepancy, Charles and Mary Lamb felt obliged to adjust their version of the story to cover up the inconsistency. Here's how they fudge the tale [my underlining].
"The story of the play was of a murder done in Vienna upon a duke. The duke's name was Gonzago, his wife Baptista. The play showed how one Lucianus, a near relation to the duke, poisoned him in his garden for his estate, and how the murderer in a short time after got the love of Gonzago's wife."
  - Charles and Mary Lamb, Tales from Shakespeare, Dent, London, 1906. p.270.

In his 1964 production of Hamlet, Tony Richardson also manages to equivocate on the parallel by changing Hamlet's line to read, "This is one Lucianus, brother...nephew to the king."  As played by Nicol Williamson, the word "brother" appears to be a slip of the tongue which is immediately covered over by the correct text. It is nonetheless an equivocation which is clear to the audience.

Imagine how the distorted parallel would have been read by Gertrude. According to Wilson's reading of the mousetrap scene, while the events prick Claudius' guilty conscience, they have a much different effect on Gertrude. Wilson concludes that she had no knowledge nor participation in the murder. "Of that she is entirely ignorant, as is proved by her words to Hamlet later in this same scene" [the closet scene]. Given, then, the long list of Hamlet's veiled and not-so-veiled threats against Claudius, Gertrude concludes that this dramatic depiction of the murder of a king by his nephew is intended to dramatize yet one more violent threat. This contributes to her inclination toward terror at the seeming violence of his madness in the closet scene.

This supposition on Gertrude's part would have been even more pronounced by other participants in the play scene who were more distanced from the central players; particularly members of the court in attendance, and the players. Here's how the Welsh critic, John Wain describes the events of the mousetrap scene as viewed from the viewpoint of the court members.

If Hamlet could have controlled his terrible inner agitation sufficiently to sit quiet and watch the king's face, other people would have done the same, and the business of undermining Claudius would have begun without Hamlet's having to show his hand. As it is, Hamlet cannot keep silent for a moment...

'This is one Lucianus, nephew to the king'. Since there is no evidence in the play itself that the poisoner is in fact the king's nephew, the detail is evidently invented by Hamlet -- or, more precisely, forced out of him by the pressure of his hatred for Claudius, the usurper who sits so temptingly close by on the throne that should be Hamlet's, side by side with Hamlet's mother who has forgotten his father. Under these circumstances, it amounts to a threat.
 - John Wain, The Living World of Shakespeare, St. Martins Press, N.Y. 1964. p.152.

Arthur McGee carries the question of the appropriateness of the parallel even further by considering how the players, themselves, would have taken Hamlet's intervention in the scene. His conclusion is as follows:

The Players indeed not only consider that Hamlet has insulted them, but that he is mad and wants to kill Claudius -- what else can they think of Hamlet's 'dozen or sixteen lines' which must be Lucianus' speech before he poisons the king?
  -- Arthur McGee, The Elizabethan Hamlet, Yale Univ. Press., New Haven, 1987. pp.113.

That Hamlet appears to be threatening Claudius is confirmed in the immediately subsequent scenes. Gertrude's response to Hamlet's apparent rage in the closet scene is built on a fear that has already taken hold.

What wilt thou do? Thou wilt not murther me?