I personally see two points of parody here.

1.
Emily is such a nature's child. She breathes, not air, but nature. Be it the beauty of nature at dawn or sun set, the glens or the forests on the slopes of the mountains.
The description is detailed and unvaried 8[

(Clermont adopts the same strategy)

Beechen cliff is described to us in some of the words (I am glad not all) often used in 'Udolpho' - coppice, verdure, the pituresque, the summit of a cliff, rocky fragment (LOL), forests, trees etc.

Catherine's knowledge was obtained from here, no wonder;
'..appeared to contradict the very few notions she had entertained on the matter before. It seemed as if a good view were no longer to be taken from the top of an high hill, and that a clear blue sky was no longer a proof of a fine day...'

Emily always found the view from the top of a cliff very splendid. She often gazed at the view from her window in the castle, which was on top of a hill.
I'm not sure about the reference to 'blue sky' though.

And so I laugh when finally Catherine is so convinced by Henry's and Eleanor's conversation that "... when they gained the top of Beechen Cliff, she voluntarily rejected the whole city of Bath as unworthy to make part of a landscape." Ha!

2.
Catherine's remarks at the beginning of their walk;
“I never look at it,” [..]without thinking of the south of France.”

“You have been abroad then?” said Henry, a little surprised.

“Oh! No, I only mean what I have read about. It always puts me in mind of the country that Emily and her father travelled through, in The Mysteries of Udolpho.

Mrs. Radcliffe had never been to the places she described in 'Udolpho'. It seems she described the scenes from paintings etc. And sometimes got it wrong - like the cafe's around Markus Platz.
We know that JA never wrote about anything she didn't see herself, or knew about personally.