> the gif you saw makes it look that way.

Makes it look what way?

Watch the NASA video carefully. It's clear that, even before the "loop" begins, Artemis is slowed down and is soon going to reverse direction relative to Earth. Which of course it would anyway, as you say--because, as the video you linked to points out, it doesn't have Earth escape velocity. The TLI burn gave it just enough velocity to reach the Moon's orbit with a little extra speed left over to get it about 4000 miles further.

But what would not happen without the Moon there is the "backwards" part of the loop--the part that took Artemis around the far side of the Moon. The Moon's gravity is what did that. In the Moon-centered frame in the video, yes, it looks like just a slight deflection--because that frame is moving with the Moon, whereas Artemis was moving backwards--in the opposite direction from the Moon in the Earth-centered frame.

Without the Moon there, Artemis would never have moved backwards, relative to the Moon's orbit, at all. Its trajectory in the Earth centered frame would have been a simple ellipse, with a maximum altitude from Earth a little higher than what it actually achieved (since the Moon's gravity did pull it back a little bit).

> This is incorrect

No, it's not. You aren't responding to what I actually said. See below.

> the “free return” would have happened if they launched entirely in the wrong direction.

But it would not have been a free return that let them see the far side of the moon, which is what I said. The Moon's gravity is what made that possible. And that was very significant.