If you were to flip the direction of the magnetic field in the above picture, it would describe light propagating in the opposite direction—so no, in this way, its direction is not a convention.
However, it's important to keep in mind that the direction of the magnetic field is a convention at a more fundamental level. It represents an oriented plane perpendicular to its direction via an orientation rule. If we all decided to use the "left hand rule" instead of the right hand rule for the cross product, then the magnetic field would point in the opposite direction. It is a bivector, or a pseudovector, field.
The electric field is a true vector field. At least in the three-dimensional description, which is itself a (very decent) convention, as long as we acknowledge that this picture depends on our reference frame.
In the four-dimensional picture, the direction of electric and magnetic fields at any point in spacetime can be described as two parts of a single oriented plane, such that a choice of reference frame determines their splitting into independent "timelike" (electric) and "spacelike" (magnetic) planes.
That may be more than you were originally looking for, but I think this question makes for a good entry point to many of the other choices of representation that we make in physics.