The applet makes the following assumptions:
The applet displays everything in only two dimensions. These are represented by an x and a y axis. The charge-carrying wire is laid out along the x-axis and the field points at which the electric field vectors are simulated lie in the x,y plane, as do the field vectors themselves. Therefore the z-coordinate of a field point and the z-component of any electric field vector are zero always and are simply omitted, for brevity's sake.
Restricting everything to the x,y plane involves no loss in generality because of the rotational symmetry of the electric field around the wire.