If "classes" means different lessons, is the word "meet" used correctly, since usually "people" instead of "things" are put before "meet"?
When you put it that way, I can see why this would read oddly.
In my thesaurus, meet is listed as a synonym for convene. In the context of education, class meets is a "shorthand" way of saying students registered for the class meet, and, classes meet at 9 o'clock is another way of saying, classes convene at 9 o'clock. Similarly, class will meet in Room 222 is the same as class will convene in Room 222.
I had never thought of this usage as idiomatic or phrasal until you asked this question, but, after reading the dictionary's definition of meet, I can see why this might sound like a misuse of the word to a non-native speaker. Nice catch. I assure you, though, this usage will strike most native speakers as perfectly normal and natural, at least here in the U.S.