Yes

While the text is poorly written and never actually specifies how the arms work, the arms don't have some of the rules for attacking with them that one would expect weapons to have (i.e. a damage die). Furthermore, the ordinary method one uses to attack with one's body (which the Astral Arms are a part of) is by making an unarmed attack. Since the arms literally do not function as written if they aren't unarmed attacks (I mean, you can substitute your martial arts die for the damage die if you want, but you don't have to), it makes a lot more sense to treat attacks with them like attacks with your regular arms-- as unarmed strikes. Furthermore, this fits well with description of the arms as part of the monk's astral self, their "true form".