Something I'll miss about AIM and older chat clients is how compact they were. Most of these newer chat programs seem to assume you're going to have their application take up the entire screen.
Most modern audio players have the same issue. WinAmp/XMMS took up very little of your screen, while most modern players will assume that full screen is what you want.
Maybe its because I don't know what I'm missing, but I didn't start using Winamp until version 5, and I think its great. Sure it has a lot of unnecessary or even broken features (looking at you audio converter), but those are easy to ignore and you can even remove some of them.
This is one of the (few?) things that iTunes gets right. Though it's a little hidden, the entire program can be minimized into a small floating album cover.
And if that's not small enough, you can minimize it altogether and just get updates and controls via Notification Center.
Sorry, but I see nothing minimal in their screenshots [0]. Same iTunes for my taste. I do believe the performance footprint is minimal, but that't not the first aspect for an everyday app.
Funny, I'm the exact opposite. Most of the chat programs I use (or have used) use the combined approach. Telegram, Facebook Messenger, and so on all have the "buddy list" permanently attached to the conversation window such that you can only see a single conversation at a time. I prefer the MDI of yore since I can have multiple conversations open at once (on desktop, I realize this isn't feasible on mobile).