I've not had (or tried to make) one yet, but here's my best guess. That particular company uses a syrupy concentrate for other fruity beverages (strawberry is what comes to mind, for the strawberries and cream frapp). So I'm guessing they have that in blackberry now.
They also use a green tea powder, matcha, and of course the cream-based frapp mix.
My best guess is, they use the syrup, the matcha, the frapp base, and the ice in normal frozen drink proportions, and then top with whip and a blackberry drizzle, which is most likely that same syrup in a drizzle bottle.
Hope this helps!