This is a description of how electromagnetic forces on moving charges differ from the forces found in non-relativistic Newtonian mechanics. (Electromagnetism is an automatically relativistic theory, and the existence of magnetic forces is actually a relativistic correction.) Newtonian forces obey not just Newton's Third Law (that the force on $A$ due to $B$ is equal in magnitude and opposite in direction to the force on $B$ due to $A$); there is also a "strong form" of Newton's Third Law, which states that, in addition, the direction of the forces lie along the line connecting the two bodies. This additional condition is needed to prove, for example, conservation of angular momentum for rigid bodies.
For charges moving in the same direction, this says that they obey the weak form of Newton's Third Law but not the strong form. The forces are equal and opposite, but they do not point along the direction from one charge to the other. (Note that the satisfying the strong form is actually not even possible in a relativistic theory! To identify the vector connecting the charges, you need to specify the locations of the two particles, which have a spacelike separation, at the same instant in time. Since different observers disagree about simultaneity of separated events, it is impossible to enforce the strong form in a relativistically invariant fashion.)
The second part says that, for charges in more general motion, even the weak form of Newton's Third Law fails. Specifically, it talks about two charges moving in perpendicular direction in a plane. When charge $A$ is located directly ahead of charge $B$, $B$ will feel a magnetic force, but $A$ will not.
The failure of Newton's Third Law seems to indicate that momentum will not be conserved. And, indeed, the total momentum of a group of charges in motion is not conserved. To salvage the conservation law, you need to also include the momentum of the electromagnetic field. The same argument applies to angular momentum; when the strong form of Newton's Third Law fails, only the angular momentum of the charges plus the angular momentum of the field is conserved. These are general properties of theories with continuous dynamical fields; the conservation laws generalize fully, but Newton's Third Law typically does not.
