Furthermore, my customer already has a website displaying that font, but all i can find in the css is a regular font-family property. There doesn't seem to be any @font-face. This would mean any user's browser would display a different font when the one intended isn't installed in his font library. Yet it does display the right font on a computer where the font is not installed. I don't know why this is or maybe i'm just missing something.

Hi,
It seems your message was cut.
Half the infos are missing.

"furthermore" => Why furthermore ? You don't say anything before that
"that font" => which "that" font ?
"a website" => please be more vague, "a website" is really too precise

What is your real question?