why is there que llegas tarde and not que no llegas tarde? Does the person wanth him/her to come late?

Hola Emanuel 

This sentence:

It is as if we were saying "I am warning you that you'll be late!

so we need it in affirmative.

You could also say:

In this case you need the negative because the warning is about "Not getting there on time".

I hope this clarified it.

Saludos

Inma