In Shakespeare's play, Hamlet observes that a king may travel through the guts of a beggar; what theme has he suggested?

In Shakespeare's Hamlet, there are a
great many word games. Hamlet is pretending to be mad and trying to throw off his
enemies, primarily Claudius, and incidentally the spying Polonius. Sometimes he says
nonsensical things. However, as foolish as Polonius is, Shakespeare, ironically, uses
the old man to speak words of great wisdom (as seen when he gives "life advice" to
Laertes). Polonius watches Hamlet carefully and notes that there seems to be some sense
in his insanity.

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Polonius:

[Aside]
Though this be madness, yet there is method in't.
(II.ii.210-211)

Hamlet plays
these games when the King and his men try to find Polonius' body. Here Hamlet puts life
and death into perspective, stating that in death, everyone is equal. He is saying that
a King can be reduced the status of a beggar in death, and he may be motivated to say
this based, finally, on his realization that Claudius
is guilty of murdering a king, Hamlet
now has proof, and that Claudius dies as has Old Hamlet with God's
blessing.

In some ways it's almost
paradoxical that Hamlet can place king and beggar on the same level, after his earlier
praise of mankind, but he has changed seeing life through the eyes of his murdered
father:

What a
piece of work is a man! how / Noble in
Reason! how infinite in faculty! in
form and / moving
how express and admirable! in Action, how like an /
Angel! ...how like a God?...and yet to me, what is
this / quintessence of
dust? Man delights not me...
(II.ii.303-307)

Hamlet places
a king and a beggar on the same level or "plate." The remains of each are equal, "two
dishes, but to one table." He discusses how the remains of a king, eaten by the worm,
and the worm by the fish, may be food for a peasant, alluding to the theme that death is
the "great equalizer." And because this is a revenge play, his hidden reference to
Claudius' impending death, will end not only the King's life, but his
aspirations of power. When Claudius killed Old Hamlet, Hamlet's
uncle forfeited his life—but he will also lose his throne and his sense of his own
importance: it is for this power that Claudius committed the
murder. Hamlet is now convinced he is morally obligated and righteously motivated to
take the King's life.

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Your fat king and your lean beggar is but
variable service, two dishes, but to one table. That's the end....A man may fish with
the worm that hath eat of a king, and eat of the fish that hath fed of that worm...
(IV.iii.26-28, 30-31)

The
themes I see here are "death as the great equalizer," driven by the theme of Hamlet's
ultimate act of revenge for his father's death.