Please don't start a debate on whether or not a machine is a person :(
They're self-aware machines created by humanity. Whilst they may be granted citizenship in the Tower, let it be known, they are still machines.
In the original leaked story he was wearing a mask, and he took it off to reveal that he was an exo. That was scrapped, and looks like it's not a mask anymore it's just the exo face.
"There has always been a Speaker, an anonymous high priest with a mysterious and powerful connection to the Traveler and its Ghosts. In all the centuries of the City's history, the Speaker's great work has never changed - to guide new Guardians, heal the Traveler, and raise our crippled protector from its slumber."
Taken directly from The Speaker Grimwoire card.
It's ambiguous.
In the dialogue, Eris is talking about how her eyes were stolen by the darkness, but she stole three back (The idea is that she has been touched by darkness, lived in it so long, that she can now see more clearly what hides in the darkness [i]"The third eye sees more keen in the dark."[/i]). It is theorized that the same applies to the speaker, that he has a "third eye" and this is how he is speaker for the traveler. The mask can be seen as metaphorical.
Either way, I guess looking at it, the Speaker being exo is my opinion more than anything else. As there's no solid writing or lore as to who/what the Speaker actually is, it's all just speculation at this point until Bungie throw us a bone.