There is nothing wrong with the looks of the font and it is not ugly. The game client uses a set of predefined rules contained in the game files called .res files to define the layout (including fonts) of the game (i.e. how it was displayed and presented to the user in-game).

I would suspect that the game client fallback to a default font as defined by the operating system if the font defined in .res file is not present in the system.

If I could recall correctly, the game defined Verdana font being used to display the text in-game. If it can't find the font installed in your system, it will fallback to a default font used by the operating system.

If you want the same look and feel as you would encounter in Windows version of TF2, install Verdana font into your Linux distribution (search on how to install Microsoft's fonts for your particular Linux distribution).

Also, I opened a more or less similar issue here: https://github.com/ValveSoftware/steam-for-linux/issues/578

Linux distributions does not include Verdana font by default because the font was owned and copyrighted by Microsoft.

Rant on
You are insulting the community by saying the font is horrible which is in fact is not, unless, the font has some kerning issue, which I didn't see from the screenshot.
Rant off

Well, lol, I didn't want to offend Linux community saying the font is horrible :) but the font is different from Windows version, and I'm almost sure it's not Verdana, but a TF2 custom font. I have thought Verdana font already installed on my machine.

Issue transferred to ValveSoftware/Source-1-Games#143.

This issue is closed - continue conversation there.