> It is the first time since 1972 that humans have travelled outside of the Earth's orbit.

They mean outside of low Earth orbit (which basically means further away than the ISS). The phrasing is not ideal.

> Earth's gravitational dominance extends 4x the distance to the moon

"Earth's gravitational dominance" is not a single thing; it depends on what kind of "dominance" you're talking about.

For example, even though the Moon is usually described as being in orbit about the Earth, its orbit is always concave towards the Sun. In other words, its net gravitational acceleration is always towards the Sun--even when the Earth is on the other side of it from the Sun. So by this criterion it's not in orbit about the Earth, it's in orbit about the Sun, doing a complicated do-si-do with the Earth, also in orbit about the Sun.

I'm not sure what definition of "dominance" you're using that extends the Earth's "dominance" to 4 times the distance of the Moon.