Here is one way to make sense of this:
Think of esse as "to be" and abesse as "to be away".
Then non procul est is "he is not far" and non procul abest is "he is not far away".
The unprefixed version non procul est makes a statement about the location only, and the prefix ab- adds a tone of being away, out of reach, unavailable.
The phrasing of the translation makes a difference.
It makes sense to say that non procul est is "he is not far" and non abest is "he is not absent", but translating non procul abest as "he is not absent far" strikes me as nonsensical.
This is just a restriction of what combinations sound natural in English.
Perhaps this is a good illustration of why I think it is best to split a translation from Latin to English in two steps:
(1) Understand what the Latin means.
(2) Express that meaning in English.
The first step is wholly within Latin, the second one wholly within English.
I analyzed the phrase you quote as a whole sentence.
If it is a part of something bigger, the translation can look very different.
This underlines the point of the previous paragraph.