In spoken languages there's an idea of "stressed" and "unstressed" syllables. A stressed syllable is pronounced with more force and emphasis. In English there are words like "permit" that mean different things when the stressed syllable changes. "PERmit", with the first syllable stressed, is a noun that means "some piece of documentation that allows something". "perMIT", with the second syllable stressed, is a verb that means "to allow something".
The pattern of stressed and unstressed syllables in the words gives a sentence a certain rhythm. It's easiest to hear if you read the sentence out loud or listen to someone else read it out. Some poetry makes use of this. Every line in the poem is written to have a roughly similar pattern of stressed and unstressed syllables, so the whole poem maintains a consistent rhythm. The idea is called "poetic meter" if you want to look deeper into it.
So the author is saying those lines are written with a sort of meter where a stressed syllable is followed by an unstressed syllable. A pair of syllables that fits this pattern is called a "trochee", and poetry written with it is called "trochaic". The words "PERmit", "REcord", and "WAter" are trochees. Phrases like "GIVE me", "SAY it", or "PET store" are also trochees.
I have to call the author out a bit on this though. Looking through those lines, most of them don't really follow that pattern. Looking at the stresses in the second line (at least how I would pronounce them in my accent):
But for THEE to DREAM such THINGS, I must BRING thee THOUGHTS of LOVE!
The line starts with two unstressed syllables, then a stressed syllable, then goes unstressed / stressed until we hit the pause. Then it repeats that pattern in the second half. No trochees there.
Or this one:
KNOW, THEN, thy MOther's JOY in CUCKolding thy FAther!
Meter is never a strict thing, but this is pushing it a bit. Out of all the lines, this is the only one I'd say fits a "stressed / unstressed" pattern:
NOW, young ROland, THOU shalt TELL me MORE of thy MOther's infiDELities!
"THOU shalt", "TELL me", and "MORE of" are all stressed / unstressed pairs. There are other parts of the line that don't fit the pattern, but enough of it fits that it seems reasonable to call it trochaic.
A lot of these lines actually fall more into "unstressed / stressed" syllables, which is called an iamb. It's a very natural pattern for English, so it's easy to fall into it even when you're not writing poetry: a common sentence like "i SAW a MOvie YESterday" is pretty much iambic. Lots of famous English poetry is written in iambs; Shakespeare, Milton, Pope, and many others used iambic meters.
