There are several elements that make John Dryden's work "Neo-Classical."
The first thing that comes to mind is the structure of his poetry and the use of vocabulary. Neo-classical poetry aims to salute the style and meter of classical poetry.This is the reason why Dryden's works often seem to be a reformation of the works of classical poets including Shakespeare himself. His writing style is uniquely balanced and clear and this is a key element of neo-classical art. Additionally, Dryden is a strong proponent of a Universally-appropriate use of the English language that celebrates the art of speaking, itself.
Another reason is because of the time of the publication of most of his works does coincide with the neoclassical school, from the 17th to 18th centuries. These were times of tremendous political changes in England, which prompted the population to embrace a new order of government through Cromwell, or return to the classical monarchy that came after the Restoration with Charles II. Artists of this generation embraced a return to the classics along with the ever-changing times.
Most importantly, neo-classical poetry is about complete thoughts, correct language, balance in usage of description, appropriate expressions of emotions, and the celebration of man as an intelligent creation. All of these elements make Dryden the quintessential neo-classical poet in literature and the arts.