The English language has incredibly many different regional accents, leading to the same words being pronounced differently by different people, sometimes in different places and other times in the same place.
What’s happening here is that some people say [ˈkʰlɪntən], such as Mrs Clinton herself, but others say [ˈkʰlɪ̃ʔn̩] with a glottal stop where the /t/ is phonemically. Those are not the only possibilities, either.
You cannot say that one accent is right and another wrong. They are simply different. It would be unnatural for someone whose accent requires one of those pronunciations to use the other one.