In this sentence, the word "gayer" (a comparative adjective) is grammatically incorrect.
Usage of Adjectives: You use a comparative adjective ("gayer") when comparing two people or groups. You use a superlative adjective ("gayest") when comparing three or more.
Context: The sentence is simply describing a general state of the students ("young... students were laughing and giggling"). It is not comparing them to another group of students.
Correct Usage: Therefore, the simple positive adjective "gay" (meaning cheerful or lighthearted in this context) should be used to describe the students.