Desktop Environments is what they meant (GNOME, Unity, other variants).

If your desktop look like similarly to the image you posted, the soft black vertical bar on the far left side of the screen is the taskbar. I think you are using Unity as your DE which is default DE for Ubuntu.

You can change to different DE if Unity is not your liking. There is a couple variants you can use, you can find them in the package manager and install it from there.

I thought the vertical left bar is a "dock".

It does not display the titles of the open windows and does not let me arrange the entries. That are the two problems I described.

It feels like this is meant to be used on a mobile device rather than on a desktop. On a desktop it makes me way less productive compared to a normal taskbar.

It is the same thing, all OS taskbar does not always behave similarly. That is Unity DE unfortunately, they are trying to "Fisher-Price" everything in there.

If you want a better taskbar/dock, try different DE and see how you like it.

That's not Unity, that's GNOME with extensions mimicking Unity.

Also instead of changing desktop environments, he could install the clean/stock GNOME session and then add Dash to Panel + Arc Menu, which would give it a Windows-like taskbar.

Unity is no longer the default DE, Ubuntu uses Gnome3. Unity has not been the default since before 18.04.

As others have mentioned it looks like like you are using the default Window Manager. You can install others that will provide a more familiar taskbar for you (that is a taskbar on the left of your screenshot). I've like LXDE and XFCE in the past, Im currently using KDE + Plasma, its only been a couple weeks so Im still learning it but might switch to another. Long story short you can definitely find a taskbar that will meet your needs for Ubuntu.

That is a launcher + taskbar. Open an app, it will show that the app is open. Open a new app, it will show there. Similar to the OSX dock.

Yes. I have been using it for a few weeks now and it sucks.

Because it does not show the titles of all open windows.

And I cannot organize the entries as I wish.

Switch window managers and you'll be able to do that.

It's great for tablets, though

/s