The two main ways to play an acoustic guitar are fingerpicking, where you pluck strings individually with your fingertips, and strumming where you hit multiple strings at once (usually with a pick, but not necessarily).

By 'broken chords' you might mean arpeggios. Basically, strumming and arpeggios are the two different ways to play chords on a guitar. With arpeggios, you pluck each string separately in a sequence.

Use these RealTracks to compare the basic styles:
Guitar, Acoustic, Strumming Ev 120 (#405)
Guitar, Acoustic, Fingerpicking Ev 120 (#522)

Beyond this there are countless variations and styles of playing, and there are many that mix arpeggios with strumming and so on.

To find a style similar to the one in your video, try entering some combination of "guitar acoustic songwriter" or "guitar acoustic folk", or "guitar acoustic fingerpicking" in the filter. I found the following one that is somewhat similar:
Guitar, Acoustic, Fingerpicking Songwriter FolkSlapQuinn Ev 120 (#2933)
There might be other suitable ones. It could also be a good suggestion for a future RT acoustic guitar style.

Andrew
PG Music Inc.