I was sizing up the new Mac Pro for mult-camera streaming, using Wirecast's solution; Matrox Multi-Ingest 4 Channel PCI card. It appears the new Mac Pro doesn't have PCI slots, so I think I'm out of luck.
You are correct, there are no free PCI slots in the new Mac Pro. They have gone down the route of external hardware via USB3 or Thunderbolt.
Alternatively there are external cages that provide PCI slots via Thunderbolt but as this is so new, not a lot of in-the-field info is available yet. And it's costly.