Is apple cider vinegar a form of alcoholic drink?

No: alcohol is metabolized into acetic acid, which is vinegar (which comes from French vin aigre - sour wine). There is no significant amount of alcohol left in vinegar - there may be a fraction of a percent, but not enough to be clinically detected or get anybody intoxicated. This is assuming it is store-bought, where testing is supposed to be carried out. If its home-made, there may be some alcohol