That isnt how I understood the video. The accelerating person has a longer spacetime path, as is moving through time and distance, compared to Alice just moving through time. But video specifies that Alice has the maximal / longest proper time, and that Bob will always have a shorter proper time due to the acceleration.
Now as there isnt a true rest, both are moving distance wise as well as time, and both are accelerated, just Alice is moving less distance and is less accelerated, which means she takes a longer proper time to get to same end point than Bob.
