No, you do not need ventilation for an electric fire. Hole in the wall fires do not burn wood or coal, so there is no release of gases into the air. Traditional log-burning fireplaces require sufficient ventilation because they need oxygen to burn. They must be connected to a chimney to filter out the gases released during combustion and prevent them from reentering the home.
However, hole in the wall fireplaces do not produce waste heat. 100% of their energy is usable, and they don’t need to be connected to a flue, chimney or vent. If you are installing into an existing fireplace you will need to block the flue to ensure there is no draft on your electric fire, as this can cause it to stop working.