Electrolytes include all ionic compounds as well as many polar covalent compounds such as acids that react with water to form ions. When you zoom in on the ethyl alcohol notice that the molecules are not attracted to either rod of the continuity tester because the molecules are not charged. When you zoom in on acetic acid, some of the molecules have dissociated to form ions. The positively charged Hydrogen ions are attracted to the negatively charged rod and the vice versa for the positively charged rod. This movement of the ions is considered conduction of electric current.
Acetic acid is a weak electrolyte because only some of the molecules dissociate to form ions.
The remaining molecules are uncharged and do not take part in conducting electric current. Each ion moves to the oppositely charged rod and again, moving charge is considered an electric current. The more ions move, the more brightly the light bulb will glow.