Are they trying to imply

No. It's speculative fiction. But they haven't entirely pulled it out of the aether.

There's long been scholarly speculation about Shakespeare's sexuality, based largely on his sonnets, many of which are romantic poems about a young man, known as 'the Fair Lord' -- and dedicated to a 'Mr W.H.'.

The Earl of Southampton, Henry Wriothesley, is one of the candidates for the identity of Mr W.H. (reversed initials). And 'The Rape of Lucretia' is definitely dedicated to Southampton.

But nobody knows for sure, and almost certainly never will. The 'Fair Lord' may not be the same person as 'Mr W.H'. Mr W.H. may not be the Earl of Southampton. The 'Fair Lord' may not even be a real person.

So, no, in short it isn't historically accurate. It can't be, because the history is unknown.