So, I found this website http://www.thealmightyguru.com/GameFonts/Letter-H.html (on the Half-Life page)
and this discussion https://www.reddit.com/r/HalfLife/comments/248tzb/the_font_used_in_the_half_life_and_and_portal
They are probably right about these fonts used in certain parts of the game HUD.
Though, it seems to me that none of these is the font used in the message texts which are made with game_text, for example: Does anyone know what is the font that is used by those text messages (in the screenshot above)?
PS: It's not Arial, as presumed.