I play a bit of that style but mostly a rhythm guitarist.  can be heard dong this

Apache by The Shadowshttps://www.youtube.com/watch?v=EzgbcyfJgfQ

It is a fingerstyle or gypsy guitar playing ( Flamenco) using picados or alternating I and M fingers ( index, middle). Classical guitarist call the action rest strokes.

You do not need a flamenco guitar to get the sound but it would be advantageous since classical guitars have more sustain and picado runs can turn out sounding muddy. 

The trick in playing picado is to make sure you alternate the fingerstrokes all the time. The only tricky part to this style of playing is  when moving between strings. Normally, when playing rest strokes the finger on the next string after playing a note and one is inclined to continue on and strike the string. That will cause you to make a mistake. Always alternate the strikes even when the notes are between strings.

cain posted:

I play a bit of that style but mostly a rhythm guitarist.  can be heard dong this

Apache by The Shadowshttps://www.youtube.com/watch?v=EzgbcyfJgfQ

He is not playing picados here but alternating keystrokes using a pick. The difference here is he is playing free strokes.