The entire galaxy rotates, it’s analogous to leaves swirling around atop a whirlpool; this has no bearing on the maximum age of anything.
And why does it rotate?
Because there are forces in it that keep all the stellar bodies from either being thrown out of the galaxy, or sucked into the galactic core.
Much like a satellite orbits the Earth, its only impulse is to move in a forward direction. It is the Earth’s gravity that bends this direction towards the Earth, despite the object’s impulse to continue in a straight line. It is called the centripetal force, and it applies just as much to the galaxy as a whole.
Now imagine an astronaut in orbit around the Earth, as analogous to a star. A baseball the astronaut is carrying is like a planet, moving along with him in orbit. But as he hurls this baseball away from himself in any direction but the direction of his orbit, it ceases to be part of his orbital impulse, and gets its own, which is either close to his, or not.
If you can imagine him on a curved plane in his orbit, if he throws the ball “downward” through the plane, even at a slight angle, it will be in a decaying orbit, and eventually reenter the atmosphere and burn up.
Only if his orbit is so high up that he could throw the baseball “up” and out of the Earth’s gravitational pull entirely would it exit Earth’s orbit and travel into deep space. Otherwise it would be pulled back to the eventual fate of a ball pulled downwards.
Importantly, this might take a very long period of time. But that is okay, because no one is timing how long whatever eventually happens to the baseball happens.
Now imagine that this astronaut is not a human astronaut, but a very long lived alien, that has been throwing one baseball a year in random directions while in Earth’s orbit, since the Earth began 4.7 billion years ago. This is much like what is happening with rogue planets. By now, the vast majority of baseballs will have burnt up in the Earth’s atmosphere, with a much smaller number still in orbit.
And the same with rogue planets, over a considerably greater period of time. Most will end up in decaying *galactic* orbits, getting ever closer to the center of the galaxy until they are destroyed, one way or another.