I don't think that the heated bed would be damaged if the connecting wire shorted out. The heatbeb is basically one large resistor. It has a couple of surface mount LEDs that lights up red when the bed is powered for heating, but there should not be other sensitive components on the board.
The greater concern I have from your attached photos, is the cause of the 'short'. Unless there was fraying or other loose wires that could have bridged the terminals, your problem might have been a loose connection that created resistance at the interface layer which then caused that specific connection to heat up. The voltage is not high enough to cause sparks across the gap.
The additional heat and electrical instability might have fried your Einsy. You don't mention if the printer starts when you power it up, but I assume that you are considering replacing parts because the printer is not working.
If you have access to a multimeter you can just measure the resistance across the wires of the heatbed. If it is broken you will see an open connection on the multimeter, but if you see Ohms in the 1-100 Ohm range (don't know the specific resistance of a disconnected heatbed), it means the board should be OK.