Ordinary sound waves don't have an amplitude defined by a spatial displacement either - they're pressure waves, where the amplitude is a measure of the change in a scalar that is defined for each position in the volume of interest (the pressure/density).
Similarly for an EM wave the amplitude is the change in a value that is defined for each position in the space of interest - the electromagnetic field strength, although this value is a vector not a scalar. (The EM field is always perpendicular to the direction of propagation of the wave, so for any propagation direction there's only one degree of freedom left which is the "polarisation angle").
Similarly for an EM wave the amplitude is the change in a value that is defined for each position in the space of interest - the electromagnetic field strength, although this value is a vector not a scalar. (The EM field is always perpendicular to the direction of propagation of the wave, so for any propagation direction there's only one degree of freedom left which is the "polarisation angle").