The heater is a purely resistive load, I think it would work. Worst case, the controller wouldn't handle it and heat up, your heater shouldn't be hurt. The heater may be too responsive to the rapid drop off in voltage, which wouldn't give you much of a control band between full on and full off, but the price is right.
The routers it was likely designed for are probably DC motors with brushes, and use current for torque, voltage for rpm.
The controller is likely an inexpensive rheostat, (variable tap resistor) in contrast to an expensive triac based dimmer, which manages power by time slicing the AC signal, or variacs, which are variable current to voltage transformers, and can raise or lower voltage.