Not to worry, the kettle is just fine! If the Stagg EKG detects that it's getting too hot (due to lack of water or other reasons), there is a physical safety mechanism that prevents the kettle from continuing to heat up.
All you need to do is add cold water to the kettle, turn off the base, and wait 5-10 minutes. The cold water will cool down the safety mechanism and restore everything to normal.
In the future, be sure your kettle is always about 1/3 full with water and only ever contains water!