According to one acid base theory the forward reaction is classified as an acid base reaction because

According the Bronsted-Lowry theory a substance as an acid if it acts as a proton donor, and as a base if it acts as a proton acceptor.

When hydrogen chloride gas dissolves in water to produce hydrochloric acid, the hydrogen chloride molecule gives a proton (a hydrogen ion) to a water molecule.

As a result of this process the Hydronium Ion is formed.