It's an alternate universe. It's not the same as ours. It's not just ''the past'', it's a different one. In this version, they don't drink the demon's blood (which is shown in the fucking cinematic itself), and after that Mannoroth appears, who is then killed by Grommash with help from Garrosh's war machines.
They create their own Dark Portal, rather than letting Gul'dan create his; and instead of connecting it to their universe's Azeroth, they connect it to ours. Don't ask how. They just do. Magic, and all that stuff. That's why it's our problem.
In their timeline, Grom kills mannoroth alongside Garrosh, with Grom being saved by garrosh and living.
The reason we see this is because the iron horde plans to fuck up our world. But the orcs are never enslaved in their world, and they have crazy firepower, so they're gonna invade Azeroth on their own behalf now, or at least try to, that's why we go there.