The input impedance of certain devices/circuits (transformers) does not neccessarily need to match their output impedance.

Consider a 50Ω (or whatever impedance) antenna as transformer that transforms 50Ω (wire side) to 377Ω (space side).

The impedance of the antenne is not (only) given by the impedance of free space but (also) by the way it is constructed.
 
So the antenna **does** match the impedance of free space (on one side); and ideally also the impedance of the circuit (on the other side).  
Since the space side's impedance is always the same (for all kinds of antennas operated in vacuum or air), its doesn't need to be mentioned.  
Only the wire side is what you need and can care about.

The reason 50Ω or 75Ω or 300Ω or ... is choosen as antenna impedances is because of practical reasons to construct particular antennas/transmission lines/amplifiers with that impedance.