The emphasis is on ὁ Κλεομβρότου . . . ἔλεος, and that is what οὐχ negates, correcting a potential misimpression by Agis.
The verb περιτέθεικεν is the least important word in the phrase, almost unnecessary in context, but the expectation of a verb towards the end of the sentence has been set up by τοῦτο . . . ἐμοὶ τὸ σχῆμα καὶ τὴν ὄψιν.
So οὐχ is placed at the beginning of the noun phrase, ἔλεος, is the last element instead of the verb to give it prominence, and the verb περιτέθεικεν, instead of being placed at the end of the sentence, is sandwiched in so that it doesn’t stand out. The noun phrase itself, the subject of the sentence, is placed at the end, again for emphasis.
There’s nothing particularly remarkable about this: you could find thousands of examples of similar word order throughout Greek prose.
Of course it may seem odd to someone rooted in English word order, which is much less flexible because unlike Greek (or rather to a much greater extent that Greek), English word order is constrained by syntax, since word order determines the syntactic function of the words in a sentence (and this is especially true in English because so many English words can function as different parts of speech, e.g., as both a noun and a verb, unlike many other languages). In Greek, in contrast, syntactic functions are expressed largely through inflectional endings, not word order.
I doubt that Plutarch thought long and hard about the placement of the words in the phrase – it undoubtedly came naturally to him as he put his thoughts on paper. And for the Greek reader, the sentence would have unfolded in a perfectly natural way, too.
To capture the effect of the Greek word order in translating, we would have to write something like: "It is not pity for Kleombrotas that has placed this dress and appearance on me; rather . . . " Not "pity for K. did not place . . . "