there is no side in space
Yes, do to an awful internet video.
There are several directional references available, obviously. Two obvious and important ones are the plane that contains the earth's orbit, the ecliptic plane, and the other is the one containing the equator, the equatorial plane. The line of intersection of these two planes is called the line of the nodes, or the Vernal Equinox direction. The line from the center of earth to the center of the sun at the equinoxes is (approximately) the VE direction in March, and opposite it in September.
It isn't clear whether the article implies that the rotational axis changes with respect to ecliptic, or whether the rotational axis changes with respect surface of the earth. It has been known since the 19th Century that the axis of rotation of earth "wobbles" with a period of about 14 months and an amplitude of about 20 meters, measured at the surface. In other words, the rotational axis is displaced from the conventional North Pole by that amount near the north pole. Google "Chandler Wobble". It has been known since about the second century BC that the rotational axis of the earth precesses around a line perpendicular to its orbit (though back then they thought it was the sun's orbit) with a period of about 26,000 years. The celestial north pole is now in the direction of Polaris, but it wasn't 2,000 years ago, and will not be in another 2,000 years, but will return in yet another 26,000. Google "precession of the equinoxes"
Right... like asking slow joe to stand in the corner, in the oval office... actually, that might be fun to watch.