Notice the murals beneath the ring. Starting from the rightmost, the pillar in question is opposite the third mural. So, if Lara wall-runs beyond this mural, she will not make it.

Once you catch the ring, stop swinging. Climb down/ up the Grapple line until Lara reaches the bottom of the second mural (which is beneath the ring). Position the camera opposite the wall (as the screenshot above) and start the wall run by pressing Left and Right.

When Lara reaches the decorative border above the third mural, she is at the perfect spot; the pillar is just behind her. At this point, press the Down direction key along with Jump. Lara will jump backwards and land on the pillar.