My speculations so far:
Playable races/classes
Space Marines = Black Templars (so far the only seen order)
Normal Space Marine
Technicus (fights the demon at 0:36 together with the space marine - i don't think that's a NPC)
Psyker (watch closely at 0:57)
Scout (0:51)
Orks = Bad Moons (the big skull at 0:15 has a little moon on it - and in general those orks look pretty yellow)
No idea which classes.
Chaos Space Marines = Khorne worshipers (Khorne Marines and Cybots - Khorne Marines and Cybots everywhere!)
Berserker
Cultist
Vehicles
Seen in the Video
Space Marines/Chaos
Bikes
Maybe Jump pack?
Titans (although i don't think you will be able to control these)
Orks
Pikk-Upz (Multi-Mounts/Players transport Players?)
Deffkopta
Logical compensations
Space Marines
Rhino
Maybe Stormbird?
Chaos
Chaos Rhino
Something that flies

Orks
Stormboyz Backpack
Some trailer analysis concerning troup transporters
I am pretty sure that Pikk-Ups (transporters) will be controlable. Why you ask?
Watch very very closely at 0:41. There is a Pikk Up driving on the ground. First of all: I don't think this scene is scripted. I think it was made for the trailer. But that's not the reason why I think the you can drive the troup transporter. It's simply the following:
First Hint:
You can see a little delay like a lag on the Pikk-Up just for the split of a second. Of course the movement of NPC-Objects can be affected by your ping, but this just really looks like a moving player-object and a bad ping on the part of the Deffkopta-Player.
Second Hint:
If you stop on 0:41 you can see a second Pikk-Up behind the first one. As you can see the landscape around those Pikk-Ups is very undulating. Now go to 0:47.
Two Pikk-Ups driving through a canyon. It's definitely the same zone, just another place.
Honestly: I don't think Vigil filmed two scripted vehicles driving miles through the desert without having the control of them.
So we can conclude that at least engine-wise it's most likely you can control troup transporters with up to 4 people (look at 0:47 again and count those boyz - one driver, one gunner, two on the back seat [you can only see the gun of the left one, the right one can clearly be seen]).
So while it's not said that those transporters will make it into the game it seems like it IS possible to control them.