Whoever wrote that short definition on the glider doesn't understand geometry.
Yes, it is an updated version of a rocking chair, but as Twoballcane said, it's much easier on the floor and has a less-pronounced "rock". And the motion does describe an arc or some single line curve; depending on the following....
The basic layout of the linkages is a trapazoid; however, the lengths of the "opposite" side links and upper/lower members as well as the mounting points can be varied to change the path of the seat.
On a typical glider, if you made a small X on the side-board, then watched it through the forward-rearward motion of the seat, you'll see it describe an arc or curve.
It would not be an ellipse or some other closed-end curve because the forward displacement is the same as the rearward.
Here's a Patent that shows a basic layout.
On the first page, there are many more Patents which can be viewed on Google's patent site.