It is difficult to argue against this Harold Bloom quote as, along with staple stage performances, there are multiple movie versions of Shakespeare's plays available. Shakespeare continues to be a source of inspiration in current culture.
Shakespeare is at the center of Western culture. This can be argued as being a detriment to the growth of theater, sustaining an image of theater that is anachronistic with contemporary culture (although film versions and adaptations strive to rise above this).
So, how did Shakespeare become cultural currency giving a person cultural authority in context of literature? While part of Shakespeare's cultural power has to do with his popularity among admiring Enlightenment thinkers, like Goethe, Shakespeare's power also is rooted in British Imperialism and the spread of the English language.
Imperialism is not only a political function, it is also a cultural function because the imperialist's culture is carried in transported social structures and in transported language, which often becomes the language of education as happened during British Imperialism.
Shakespeare became the golden standard for the expression of the English language. Since English has been transported to all corners of the world and to all generations through English based education, Shakespeare has been a global cornerstone of English. The book, Political Shakespeare: Essays in Cultural Materialism, has many essays on this topic.