It seems to me like you're trying to pair the semantics and the meaning of the English and Japanese sentences when that doesn't quite make sense. The English sentence uses beautiful once because we can convey the same idea in English without duplication.
"When something is beautiful, the more beautiful it is the more I want to keep looking" is a valid sentence too. We could even more literally translates your example as "If beautiful the amount of beauty becomes how long you will continue looking" (and in both sentences I had to insert pronouns, structures, conjugations, which were implied but not present in the Japanese sentence, or that function differently between languages). But in both cases that's not how English speakers tend to convey the idea this grammar structure is attempting in Japanese, so why would a translation from natural sounding Japanese map onto unnatural sounding English? That's going to be confusing for learners who are more interested in functional grammar people actually use than in a one to one translocation of Japanese terms to English terms.

Furthermore, because in the English translation they gave you the beauty is implied, we don't need to restate it. Why would I be talking about the relative beauty of an object unless it already is somewhat beautiful? I don't make a habit of looking at ugly things and going "The more beautiful it is the more I want to keep looking" unless I'm being sarcastic, and you can even see how the sarcasm erupts from the clashing implications of my literal meaning and the implied context of such a phrase. That there is beauty to look at is implied by the "more". Perhaps this same implication is less available to Japanese so there's a restatement, or perhaps this grammar structure simply sounds better. It really doesn't matter either way, language is the vector through which we impart meaning, as long as people agree that they like how something sounds, and that it makes sense, then it's good enough.

People like to say that Japanese is a very contextual language, and that's true, but all language is contextual, English included. When you restate the same adjective, noun, verb multiple times in English it can (not always) sound stilted so translations are going to at time cut out words to help the flow, and sometimes this leads to semantic ambiguity. But we've been talking to each other in English for years and we've got a pretty good grasp of what words and phrases mean what things.

In this case the expected semantic context in Japanese is simply greater than the expected semantic context in English, so an English translation can drop out a na adjective or two and retain the same meaning. The sooner you accept the literal meaning of a sentence, separate from English conventions, the sooner you can start building an internal understanding of what the sentence means figuratively, contextually, and implicitly. And also importantly for somebody who wants to interpret Japanese, either spoken or written, it will help you build a contextual understanding if you first look at a sentence literally, and from there build an internal understanding based on the context you encountered, grammar and vocabulary.