In the original comics, the second soul Death visits is a struggling standup comedian who does a routine about Batman (who is, of course, a real person in the universe of the comics). This has been replaced with Sam, the swimmer.
There was a White Horse pub on Poplar High Street which is close to the location in Docklands implied for the meeting place of Dreams and Hob. The pub was demolished in 2003, which approximately matches the timeline shown. Archaeological remains showed that there was history of brewing on that site going back continuously to medieval times. The pub was most famous for being run by two women In the 1740s who presented themselves as 'Mr & Mrs How'.
Several literary figures are depicted at the inn throughout the centuries, including, besides William Shakespeare, Geoffrey Chaucer and Christopher Marlowe.
This episode is a compilation of two "breather" issues from The Sandman comic book series, issue #8 "The Sound of Her Wings" and issue #13 "Men of Good Fortune." In comics or TV/streaming entertainment, a "breather" issue or episode indicates a stand-alone storyline where characters may be influenced by events, but no part of the plot continues past the issue or episode.
The dialog with Will Shakespeare (both with Kit and with Dream) is written in iambic pentameter.