The tabs you provided are in Drop D tuning (which it clearly states at the top of the sheet). Drop D tuning means dropping only the lowest (6th) string from E to D. Make sure you take that into account.
Just from looking at the first few seconds the audio is an entire octave higher than the tabs you listed. That means the notes should be played like so:
Also of note is that the temp is around 140BPM, not 120BPM like the tabs indicate, and the instrument used is probably not a guitar. If it is it would be a steel string guitar instead of a nylon string guitar which you probably have. Steel strings give off a different tone and are generally cleaner and ring better than nylon strings. Those tabs are also...not the best quality.