Unfortunately no it can't happen.
Let's say the gravity is high enough to pull people off Earth and into the Rogue Planet, they would then be falling at terminal velocity to the surface of the RP, the problem with trying to land on your feet at terminal velocity is that it tends to be somewhat terminal...
Ok so let's somehow take the terminal velocity splatting as handwaving-ly survivable. And let's also assume that the RP is going somewhere in the region of 525km/s then the atmosphere would have so much friction between the two that it would turn into plasma that somehow your people need to survive traveling through...
Along with some of the Earth's atmosphere being ripped off with you, make just a small amount of catastrophic turbulence that no aircraft could survive let alone a person out for a morning run.
Even if we assume that the RP is roughly 5x the diameter of the earth (assuming this based on a rough estimate from your pictures) then the gravity would be crushingly strong once the people land there and would be immediately crushed by their own weight.
AND then there is the fact that even with how small Earth is by comparison it would cause huge earthquakes and general doomsday situations on the RP to make habitability quite unlikely once landed
EDIT: Only potential chance of survival
The one chance of people surviving would be if there were anyone on the International Space Station (ISS), and it was in the perfect place, it might... I stress might be possible that it could get dragged out of Earth's orbit into the RPs orbit, however, the velocity change would rip it apart, but perhaps maybe just maybe if a couple of the crew were in the Return capsule with a heat shield, then they have a chance of survival until they reach lower altitudes and are crushed at least