이치 is a noun meaning 'the way things are'. So 변하는 게 세상 이치잖아 means "To change is just the way things are." I'm not sure it's clear enough.

It's probably useful to know how it takes that 이치잖아 form. 1.변하는 게 세상이치(이)다. 2. 변하는 게 세상 이치지 않아. 3. 변하는 게 세상 이치지 않아?. 4. 변하는 게 세상이치잖아? Note that 이치다 in #1 is a contraction of 이치이다 (이치(the way; working principle) + 이다(is)). 이다/이야 contracts to 다/야 after a vowel-ending syllable (or syllable with no 받침, consonant in the bottom position). #2 is the negative constructed as ~지 않다/않아, and #3 the interrogative form of it which has no change in wording. #4 shows that ~지 않아? contracts to ~잖아? So ~잖아? is a question in the negative of #1.. Such constructs are a common way to actually mean the positive "is/does" while asking confirmation, by asking the negative rhetorically. If it's said strongly with a tone of annoyance, it will carry a strong positive meaning. You see such phrases all the time, especially in conversation. - 너 고기 싫어하잖아? ( = 너 고기 싫어해) = I thought you don't like meat. - 너 약 벌써 먹었잖아? 왜 또 먹어 = You already took your medicine. Why take it again? Sometimes they can change meaning very subtly. 1. 너 그 사람 좋아하잖아? = You love that guy, don't you? (= I understand you love that guy). 2. 너 그 사람 좋아하지 않아. = You don't love that guy (in my view). (하잖아 in #1 is said quickly like a single unit, while 하지 않아 in #2 is said more slowly and clearly) Because the negative form can mean the positive in ~잖아? (it's tone is also only slightly different from other positive sentences), we usually don't contract it but leave it as ~지 않아 (and pronounce the 않아 part more clearly) when we really mean the negative, as in #2 above.