Is there a word for Chinese songs that rhyme like Jay Chou's 迷迭香 and JJ Lin's 伟大的渺小?
We call it 单押 in Chinese，which means that sentences have the same or similar vowels between sentences. The end of each sentence has the same vowel. It's a type of rhyme scheme，not a type of music though. You can find it in many types of music.
Here's some other examples:

东风破 (by Jay Chou),
一路向北 (by Jay Chou),
禅舞不二 (by Wilber Pan).