I'm not even close to being a master of the Elder Scrolls lore, but could it be that races only starting traversing to other provinces after the Imperials took control of Cyrodiil and started the empire? Because this game is 1000 years before Skyrim, and before the empire, could it mean that races didn't do much inter-province traveling because they each had their own sort of kingdom in their home province?

No. The lore does not support that stance at all. Besides, because of the factions, interprovince travel is already happening. There were also two empires before the Septim one.

Ah okay.

How did you manage to play as an orc in Daggerfall?

How did I manage to miss that tidbit. Maybe you were playing as an Imperial in Daggerfall?