After the King leaves, Hamlet's insane clapping draws a hateful look from Polonia, who in this universe, is Claudius' lover. The transgendering of Polonius has several effects, but one of them is creating a dynamic that makes attacks on Claudius that much more personal for his councilor (and chief accomplice?). The King obviously "blenched", and Horatio really did note him and shares in Hamlet's joy. There is no bitterness in them, Fodor treats this as a victory as yet untinged by what must come after. When Hamlet calls for the recorders, it's in a gently mocking, celebratory tone, a way of smoothing over the fact that it's a clarinet and not a medieval recorder he finds. It's amazing how an actor can simply put a little humor or sarcasm into a single word and modernize it immediately.
Rosencrantz & Guildenstern, dangerous bullies in this world, are really angry and do a lot of shouting out of their frustration. They're at the end of their ropes. In fact, their reaction is so strong that Hamlet's "I am tame" shames them into a quieter stance. They're the ones who seem crazy, not him. Instead of the aggressive, threatening madness most Hamlet put on in this sequence, this one instead goes for innocent playfulness, as a man-boy who doesn't understand why people are angry at him. Ever his partner in this affair, Horatio quietly smiles next to him, somehow acting as Hamlet's irony. It's how R&G know they're being laughed at. No matter how much they threaten him with body language and tone, Hamlet doesn't lose his composure. On "as easy as lying", he makes it a discovery, an answer inspired by looking at them. And there's no violence in the business with the recorders. He just gives them the clarinet and begs them to play it, more a petulant child than a dangerous man in his own right. They hesitate before admitting to not knowing how and roughly disassembling the instrument before giving it back, again an implied threat.
By the time Hamlet gets to "you cannot play upon me", Polonia is standing behind R&G and the remark is addressed to her as much as to them, if not more. Through the innocent act, he lets slip that he knows they're all in league with each other. The imaginary cloud in the ceiling plays out as a power struggle, Polonia refusing to be intimidated, her responses dripping with sarcasm to let him know she's quite aware of what he's doing. There is further osmosis between the conspirators at the end of the sequence when "by and by is easily said" is spoken to R&G instead of Polonia, but they put a further twist on it. R&G each get one "by" thrown in their direction, making it "bye" and "bye", a pun on their quick dismissal directly following.
Horatio then leads him out of the room by the hand, a gesture that could be interpreted as either romantic or childish, but a tense sound stops him. Does he feel the Ghost? A gun left on a chair - it might have fallen out of R&G's pockets - draws his attention, and he fondles it as he says his speech, a prayer to the gods of violence. These choices are informed by the modern staging of the play in the film. Hamlet does not carry a weapon, so much procure one. And the "witching hour" cannot be heralded by bells or some such, so a strange feeling comes upon the Prince instead. It's a supernatural occurrence, this weapon suddenly materializing when Hamlet needs to kill the King, and supernatural forces may well be at work.