Unless you know some way to preserve that molded fine grain on the plastic's surface, I believe you will only produce a larger and larger scuffed area as you proceed. At best, you can use finer and finer polishing agents long enough to produce a uniformly smooth shiny surface (on the plastic portion) destroying the matte appearance, but it will take some very careful work to prevent ending up with anything but a gray-white sanded-looking surface. Some sort of solvent may smooth up the surface, but the end result may be worse than what you started with.
Re-molding by heating to resurface the piece is not a realistic approach, unless you have an upholstery shop with the right eqipment.
IMHO, the best you can do is remove the piece, or pieces, and either replace them, or stretch a piece of sheet vinyl around them, carefully and tightly molding and gluing it to all surfaces so as to make a reasonable duplicate of the original contours, using vinyl glue, epoxy, or possibly contact cement, and carefully trimming. This is far and away the best choice for resurfacing the vinyl portion, IMHO, preferably replacing the vinyl and padding.
A less involved option would be to glue a thin strip of flat plastic,rubber, or vinyl along the bridge of the plastic portion, making sure it is wide enough to cover the damage. If the scuffing is very minor, gluing a clear piece of vinyl, matte if possible, or shiny if you like the effect, over it to possibly cover the damage while being a sacrificial surface that still shows the original color and pattern while protecting that surface. Covering the whole piece, as mentioned above, is still your option with the clear vinyl.
Lastly, there are plastic/vinyl sprays, but I think the other options will give you longer results, and painting may not give you the appearance you will like. Of course, the covering methods assume you can match the color/grain of the originals.
Others, particularly the professional upholsterers on this forum may know better methods, but I think replacement still looms as the best for the plastic part, cost not a factor, but re-covering the vinyl part is right up there with replacement of that item, if only end result is considered.
Just my 2 cents worth.