There are two things that tend to make us individuals, our intellectual thoughts and attitudes and our personal relationships. Both of these are essentially nonexistent in this book. Because people have lost the ability to have either of these, they have also lost their individuality.
If you have no intellectual life, you have no real thoughts. You might as well be some lower form of life if you are just walking around existing and looking for fun in the parlor walls, amusement parks, etc. Because people in this society have no books, they also have no intellectual lives and no real thoughts and opinions. This means they have lost a major way to be different from other people.
In addition, the people have lost the ability to be close to others. We see this in the lack of any sort of caring between Guy and Millie and in the attitudes of Millie's friends towards their families. When people are no longer able to care about one another, they also lose a part of their ability to be individuals.
With no emotional lives and no intellectual lives, the people in this society have lost their individuality.