What distinguishes modern poetry from prose?
The Wikipedia article on Chinese Poetry is particularly bad, without a single source given for the paragraph on Modern Chinese Poetry. The article on Modern Chinese poetry is equally bad, with most of the references given to a collection of English translations compiled in 1970.

If you're really interested in the subject, try Michelle Yeh's book "Anthology of Modern Chinese Poetry". Although it is now 20 years old, it is still a good survey and will give you a fairly clear idea of what modern Chinese poetry is like and how it has evolved.

If I had to name a characteristic of modern Chinese poetry, it would be that prosody (patterns of words and sound adopted by the poet) is used to give new meaning and emotional impact to ordinary forms of language. Here is an excerpt of a poem by Yang Mu (楊牧), "Let the Wind Recite" (讓風朗誦), that is typical of how modern Chinese poetry reshapes ordinary syntax

假如我能為你寫一首
夏天的詩，當蘆葦
劇烈地繁殖，陽光
飛滿腰際，且向
兩腳分立處
橫流。一面新鼓
破裂的時候，假如我能

為你寫一首秋天的詩
在小船上擺盪
浸濕十二個刻度
當悲哀蜷伏河床
如黃龍，任憑山洪急湍
從受傷的眼神中飛升
流濺 ...

To say that it "seems like a simple short vernacular essay" suggests a very odd idea of what a "vernacular essay" is.