In that video, the description says
xfwm4-tiling. So it's not just XFCE (and xfwm) doing that. It's an additional package. apt-cache search doesn't find it, so it's not in the Ubuntu repositories. Video description also says s/he's using Arch Linux and refers to AUR, which is the Arch repositories.
Unless you want to figure out how to compile and use it in Ubuntu, or find someone that's done that already (maybe there's a PPA), if you want that tiling behavior, you'll probably have to switch from xfwm to another window manager that supports tiling.
Above in the comments, someone mentioned you could look into using Awesome (but later deleted that comment). I mentioned you can use Awesome inside XFCE. It's actually probably easier to use XFCE apps inside Awesome than the other way around. If you install awesome using apt-get, you will find an awesome session installed in the graphical login manager (lightdm).
You can then configure awesome to autostart various XFCE apps, such as
xfce4-power-manager (important for power management functions like suspend and shutdown on low battery),
xfsettingsd (daemon which makes sure some, but not all, XFCE settings are executed, such as display settings and gtk theming),
xfce4-panel (so you can use the panel you are accustomed to),
xfce4-volumed (xfce volume daemon), etc. Awesome doesn't support compositing, but you can get that by autostarting
xcompmgr. There's a lot of info online on how to run this stuff in Awesome, including elsewhere on this site.
Here's a basic tutorial for using Awesome.
If you want to run Awesome in XFCE, that's not difficult, but Awesome needs to be reconfigured to work properly with the XFCE panel; I don't know how easy that is (my guess is it's not hard, but it's a time investment in any case).