I don't have experience with non-alphabetic writing systems, but I was under impression that for simple written communication nowadays plain text is good enough for every language supported by Unicode. I've heard e.g. about Han unification, but is it bad enough even for non-linguistic purposes?
Which features, in your opinion, are required for decent non-alphabetic language compatibility on top of plain Unicode text?
The first thing that comes to mind is things like right-to-left or top-to-bottom languages. Some ancient languages were written right-to-left and then left-to-right and then repeat.
Markdown isn't plain Unicode text. It mixes markup marks with plain text, and is intended to provide more layout than plain text. Plus, the question is rather broad, as there are so many non-alphabetic languages around the globe. I'm not knowledgeable enough to offer an answer.
You may want to read the work by W3C[0]. Some requirements mentioned exceed the needs of simple written communication, but not all in my experience. The problems usually arise when you mix different scripts.
Which features, in your opinion, are required for decent non-alphabetic language compatibility on top of plain Unicode text?