“See that you despise not one of these little ones: for I say to you, that their angels in heaven always see the face of my Father who is in heaven.” (Mt. 18:10)
Nowhere does Jesus say that only Jewish children of His time on Earth had guardian angels, or that humans lose their guardian angels as they grow older. Therefore, one must surmise that all humans have guardian angels – and that is what the Church has taught.
The Catechism says “believers” because you’re quoting a part where it’s talking about angels as part of the way the Church works today, just like earlier it talks about angels’ part in salvation history.
However, it first says “human life,” which means every single human ever is protected “by their watchful care and intercession.” And if you follow the footnote, the scriptural references show you that, starting with the same Mt. 18:10 I just quoted, which is straight from Jesus’ mouth and therefore of the highest authority. (Also Lk 16:22; Ps 34:7; Ps. 91:10-13; Job 33:23-24; Zech 1:12; Tob 12:12.)
Now, the second quote, from St. Basil the Great’s Against Eunomius (Volume III, Chapter 1) goes like this: “Likewise, all the angels, having but one appellation, have the same nature among themselves, even though some of them are set over nations, while others of them are guardians to each one of the faithful.”
This is in the context of a discussion of the nature of all three Persons of the Trinity being the same (ie, the Trinity doesn’t have three different natures of Godness). Basil is not excluding non-believers from having guardian angels, but rather emphasizing that different angels can have either very general or very specific jobs from God without having different natures; there may be different kinds of angels but they all share the same angelic nature. The Catechism is using this quote because it is a nice quote, and because it shows that belief in guardian angels is part of Christian tradition in the East as well as the West.
Obviously “believers” are better able to receive help from angels, because they have advantages in terms of knowledge and grace. (Whether or not individual believers decide to ignore their advantages.) Also, angels aren’t going to override your free will. But guardian angels are still going to be there for every single human, whether or not they believe in God or the teachings of the Church.
The Catechism tries to contextualize doctrine to give people a more sophisticated idea about how it works, and to let people know that the stuff from the “Old Days” hasn’t been ditched. It doesn’t contradict things previously learned and explained throughout the ages; it supplements that doctrine.