Tasty is absolutely an adjective. These kind of words which end with "ty" always have "three levels" to describe the level of the meaning . For example, the first level of tasty is tasty, then is tastier (more tasty) and the tastiest (most tastiest)
i don't know why those word have ty for the ending. I guess it is just the way it is
-ty is a suffix, forming nous denoting quality or condition such as beauty, royalty