I want to know if the games for GameBoy Color are considered to be 16-bit games? If not, what category do they fall under?
No, they would be considered 8-bit because this bit rating relates to the processor. Using the terms 8-bit or 16-bit for example refers to the console itself rather than the games that can be played on them.
See here for the Gameboy colour specs, you can see the processor is 8-bit.
This term could be confused with the colour palette available, which again from the link above, show the Gameboy colour to have a 15-bit colour palette. However, this is not a factor for the term in question. The increased colour palette is most likely available due to an increase in memory from previous Gameboy editions rather than anything else.