The actual effect, or at least the basis of it, is already available in Motion.
Select your Text object, then go to Behaviors > Text Basic and apply the Slide In effect.
You can also apply the Slide Out effect, but you will need to align it with the end (out point) of the Text object in the timeline. You can do that easily by setting the playhead to the last frame of the Text and with the Slide Out behavior selected, type Shift - ] (right bracket) to align the end of the behavior to the playhead.
If you want to customize the overall look of the behaviors, select one of them — the behaviors inspector should open. You will need to click the disclosure triangles for Format (to reveal the positional change parameter) and Controls (to reveal the animation controls). You may want to play with the Position X and Spread parameters *and* you might want to lengthen the timing of the behaviors to slow things down a bit.
The rest of the effect shown in the video can be done with masking... but that might be another topic for you when you get there.