Personally, I would say that the assertion is actually accurate. At least in the normal sense of the word, Artemis II is no longer in Earth orbit.
NASA, for example, provides this (admittedly somewhat simplified) definition of an orbit:
An orbit is a regular, repeating path that one object in space takes around another one.
https://spaceplace.nasa.gov/orbits/en/
Artemis II's current trajectory takes it towards the moon where it will experience much more gravitational influence from the moon than from Earth, which is what will pull it around the moon and back towards Earth.
Here's an artist's conception illustration from NASA of approximately what the Artemis II mission's planned trajectory would look like (obviously, it's not to scale):

Source: NASA
An object is normally said to be 'orbiting' another one if the other (generally more massive) object's gravity combined with the object's own momentum is holding the orbiting object in a closed (or at least very nearly closed) elliptical path around the more massive object. That's not what what Artemis II is doing right now, since they have already completed the trans-lunar injection burn, placing them on a trajectory that will take them in a figure-8-style pattern around the moon rather than in a closed ellipse around Earth.
As such, I would not personally call their current trajectory an orbit of either the Earth or the moon, as it is not in a closed elliptical path around either of them, nor anything particularly closely resembling such a path.
That being said, it does depend on exactly which definition you're using. The Encyclopedia Britannica, for example, seems to have a broader definition of 'orbit,' which could include Artemis II's current trajectory. It provides this example:
Some bodies may follow parabolic or hyperbolic paths (open-ended curves). The orbit of a body approaching the solar system from a very great distance, curving once around the Sun, and receding again is such an open curve.
Personally, I would not consider that to be an orbit, since it is not a closed path (and, at least in my experience, such objects are not typically said to be in solar orbit in astronomical circles.) Such a definition seems problematic to me, since such an object would be on an escape trajectory which is normally a classic example of a trajectory that is not an orbit. However, if you go by their definition, then it could be said that Artemis II is still in Earth orbit (and also lunar orbit.)