A material can affect an electric field without affecting a magnetic field: electrically conductive (versus insulator that won't affect a field so much except via dielectric effects).
A material can affect a magnetic field without much affecting an electric field e.g. ferrites are non-conducting.
A finger changes the capacitance between two "plates" and that is what is detected.
Also the attached drawing shows diamonds but I've only ever seen flat wires myself (when looking closely at touch screens you can sometimes see the transparent sense wires). But I'm no specialist and I don't know how correct the drawing is.
