For this song you'll need an acoustic guitar with steel strings. If you only have an acoustic guitar with nylon strings that'll work as well, but you'll get a bit of a different vibe. You can even play it on electric if you use a pretty, clean tone and play with your fingers.
I'm playing a Martin-style VKV acoustic with a combination of a built-in Fishman pickup and an MXL condenser mic to get the sound you that you hear in this video, and I'm picking with my fingers.