I believe you’re correct — it should be “their”, in reference to “cities”. Perhaps the author was trying to refer to “mega-city living”, but that doesn’t quite make sense, and it is really bad style to put the pronoun before the noun it refers to. Also, “more healthier” is wrong in this context. For the comparative degree of the adjective “healthy”, we either say “healthier” (usually) or “more healthy” — it’s redundant to use both “more” and the suffix “-er”. To the extent possible, you should try to read material by educated native speakers, not just any native speaker.

There are a couple problems with the grammar of that sentence. The word "its" refers to "larger cities," so you are correct, "larger cities" is plural, while "its" is singular. A cleaner way to write this would have been ". . . a concerted effort by political and business leadership, as well as the general populace. . ." The other problem is the phrase "more healthier." It's redundant. It should have been either "more healthy" or "healthier" - but you can't use both "more" and the "-er" suffix.

It is correct...if it refers to the singular 'city' - which seems to have been the intent of the author. However, it is logically and grammatically a terrible sentence.

"it's" should be "their". These sorts of mistakes are natural - more so in conversation, but even in writing unless it's been proofread. If two native speakers were speaking and there was a transcript, you'd often see the conversation dotted with missing words, bad grammar, inappropriate word choice, etc. When we're listening we do our own 'interpretation' or filling in the gaps and don't notice this. I guess what I'm saying is, it's good practice to see errors like this.