Can my opponent move units when Vex Apathetic is stunned? It says "Stun it. They can't move it this turn." Is that literal?

Yes, the text is literal. When Vex, Apathetic stuns a unit with its ability, that unit is both Stunned and subjected to a restriction that prevents it from being moved for the remainder of the turn.

Here is the breakdown of why this works:

1. Stunning: According to Rule 423.1, a Stunned unit cannot contribute its might to damage in the combat damage step.
2. Movement Restriction: The card text explicitly states: "They can't move it this turn." This is an additional restriction applied by the ability, independent of the Stunned status itself.
3. Literal Interpretation: Per RiftJudge FAQ #8746, this restriction means the unit cannot be moved by any means (such as the Standard Move or card effects) for the rest of the turn in which it was played and stunned.
4. Duration: As clarified in RiftJudge FAQ #8746, both the Stunned status and the "cannot move" restriction expire at the beginning of the next Ending Step.

In short, your opponent cannot move that unit at all while it is under the effect of Vex's ability during that turn.