Shakespeare expanded the scope of what we consider tragic events
Before Shakespeare's tragic plays, tragedy generally focused on a very specific type of hero and their downfall, but Shakespeare's expansion of tragic themes and roles meant that a large variety of events could be portrayed as tragic.
Aristotle: an Ancient Greek philosopher who developed several important theories about tragedy and theatre
Shakespeare's influence on theatre and literature is a result of his unconventional tragic plots and characters. From the way he impacted contemporary dialogue to the expectations of the audience, many regard him as the best tragedy playwright.  His works of tragedy are timeless as they do not lose meaning or influence over time. The core value of tragedy is how it affects the audience's reaction and behaviour when prominent tragic heroes move through virtuous or unfortunate experiences in the play. Each of Shakespeare's tragic heroes leave an impact on the audience by winning their sympathy, pity, or both at the same time.  Setting such high expectations in theatre, Shakespeare redefined and expanded the scope of tragedy.
Although Shakespeare certainly affected the way tragedy and tragic heroes were presented, he was not the only playwright of his era to create such an impact. Miguel de Cervantes lived in the same era as Shakespeare, but he pioneered techniques such as realism and intertextuality, expanding genres in theatre. Cervantes fought in the Battle of Lepante, giving him a realistic understanding of tragedy, which he successfully portrayed through his stories. Even Freud was influenced by Cervantes's work, suggesting that Cervantes had a much stronger influence on his audience in how he presented tragic events.
Before Shakespeare, only certain events and certain types of character were considered suitable for tragedy. Shakespeare altered this by presenting a large variety of events and characters as tragic, and breaking established conventions of tragedy. This has had a lasting effect on the development of tragic theatre, indicating Shakespeare's importance within the genre.
Rejecting the premises
Many writers were reforming tragedy in the Elizabethan age, not just Shakespeare. This indicates that he was perhaps part of a trailblazing movement rather than being extremely significant as an individual tragic writer.