From the orange portals frame of reference, the cube, and everything else in the world, is rushing toward it. So the cube (as well as the entire world around it) has a velocity relative to the orange portal.
But only the cube goes through the portal, the rest of the world does not come with it. At that point, the frame of reference changes. You can think of it like this: The cube has an velocity of X with respect to reference frame Y; once it leaves the portal, it keeps that velocity X but the reference frame changes from Y to Z. The velocity doesn’t disappear.







Alright, since you didn’t like my last explanation for some reason, let me try again.
You know how when you stick your hand out of a moving car, you feel a massive rush of wind, even if it’s not windy out? Ok, so imagine sticking a portal out of a moving car, what do you think happens to the air? Does it come to a dead stop after it exits the portal? Why not? The air itself wasn’t moving, only the car with the portal was.
Solids in this case will work the same way. It doesn’t matter if a solid is moving toward the portal, or the portal is moving toward it, what matters is the relative velocity.