Presumably for copyright reasons, Ms. Seth didn't provide the full text of the original poem (on which this theory is based);
I've found a source which provides a scan of the whole poem, for discussion purposes.
Tolkien Gateway has the 'Stone Troll' version.
Okay, so first off: it's very obvious from comparing the two poems side-by-side that the change from John to Tim came with the change in the rhyme scheme. Specifically, when editing the poem, Tolkien clearly decided to put an internal rhyme into the third line of each verse, to match the one in the first. 'John' doesn't rhyme with any good body parts; 'Tim' does.
Secondly, the identity of the troll with Shakespeare depends on assuming that it's the same troll as Bill Huggins in
The Hobbit. 'The Root of the Boot' gives the troll no name; why assume he's the same one as William, rather than Bert - or indeed, perhaps this troll is also called Tom! Ms. Seth makes no argument for her identification of the two, which means the entire case is built on 'Tom', 'John', and 'the concept of stealing'.
So let's look at the poem. Tom is there - but he seems to have that name mostly to rhyme with 'with his big boots on'. John is definitely there - but it's proverbially the most common name in English. So there's not much of a case to be built there.
And the content of the poem? Well, the first verse claims that the troll has 'seen no man nor mortal' - hardly evocative of Shakespeare's fame. Ms. Seth's 'birchyard' (verse 2) is an obvious rhyme for 'churchyard'. Verse 3 drops into a religious tone, saying that the body is worth nothing compared to the soul; Verse 4 continues this by condeming Uncle John to Hell, and Verse 5 has Tom trying to send the troll to join him. Spirited stuff! But is it Shakespeare?
It, ah... seems unlikely, frankly. Yes, you can draw links between the poem and plagiarism - but you could equally claim it's about literally any situation in history that involves someone taking something and getting away with it. There is nothing that ties it directly to the Shakespeare story, and the Shakespeare theory doesn't explain the religious angle.
Also: would Tolkien really write
this in a cunning analogy for a historical drama involving Shakespeare?
So he rued that root on the rumpo,
Lumpo, Bumpo!
hS