I love the bass tone in this clip, it's really deep and it's cool that he can get such a deep tone with a pick. I can get somewhat of similar tone with old rounds but there's always some trebly overtones unless I drastically eq the treble down, I have no experience with flats but I'm kinda guessing he might be using flats??
They sound like flats to me.
You can get some nice depth with a pick by playing up near the neck.
The bridge pickup on his bass adds some nice clarity to the sound too.
They do sound like flats, but if you listen to Interpol's albums the bass tracks sound like rounds. Not quite a thick, but more growly and more top end. If they are rounds in that clip, they're definitely very old and worn in.