It's a different way to do more or less the same thing.
The differences:
* The editor is Vim not Emacs.
* Vim is not able (without unconvincing plugins/hacks) to run a shell in a window so if you need one you are pretty much forced to run it somewhere else. Be it another terminal emulator instance, another terminal emulator window, another terminal emulator split window (like you do), in the same terminal emulator window (juggling with Ctrl+z/fg), another window in tmux/screen, another pane in tmux/screen, etc.
* Yaquake is a GUI app that you can't realistically run on a remote server while tmux is CLI-based. When SSHing, tmux is possibly the closest thing there is to Yaquake.
* Tmux and screen both allow you to attach/detach sessions which makes these tools very useful on remote machines where they are commonly used to launch servers or long running tasks.
* Probably many more…
Note that these are DIFFERENCES. They CAN be benefits, depending on your workflow and needs.
Totally OT. I know about Yaquake since years. I know about Quake since much longer. I know that Yaquake "top-sliding" UX is based on Quake's console since all those years. Yet I've just realized, now, that the "quake" in Yaquake is actually "Quake" and that, for all those years I've pronounced it in a kind of japanese-style "Yakuake". Oh well…
tmux splits shells into windows. The suggested workflow is to have vim in one split window, and other shells in other windows.
tmux has the benefit of a keybaord-driven interface to jump between terminals, so it's not unlike having Emacs running with various vertical and horizontal splits running console buffers (which is something Vim doesn't support well natively.)
It gives Vim users the kind of workflow that some other tools provide natively with a completely keyboard-driven interface.
Posts about using vim and tmux are pretty obviously not pointed at emacs users.