Why are electromagnetic waves called waves even though they don't travel through a medium?

The definition of a wave is not that it is the oscillation of a medium. Waves are called waves because they are solutions to a wave equation, which is, for a generic "excitation" $A(t,x)$ depending on the time t and some spatial coordinate $x\in {\mathbb{R}}^n$, of the general form
$\frac{{\mathrm{\partial }}^{2}A}{\mathrm{\partial }{t}^2}=c^2\mathrm{\Delta }A$
where $\mathrm{\Delta }$ is the Laplacian for the spatial coordinate. The wave equation, in turn, is called a wave equation because it is precisely the equation that governs the archetypical system where a wave occurs - that of masses linearly connected by springs.
While a wave equation may arise from considering a medium, a medium is not necessary for a wave equation to occur, as Maxwell's equations and the disproof of almost all luminiferous aether theories show.