All that tells us is that there was a man from Stratford called "Shaksper" and that, for whatever reason, the similar name, "Shakespeare" or "Shake-Speare" appeared on a number of plays attributed to him. That does not prove that he wrote them. Books were often printed without an author and often under pseudonyms. 
We don’t even know if that is how he spelt his name. The only surviving example of Shakespeare’s writing are six scratchy signatures spelt several different ways.
There is also significant evidence to suggest he did not write the plays. What we know of his education suggests that the Stratford man may not have had the necessary schooling to produce works of the calibre attributed to his name, because there is no documentation for his having attended school in Stratford, only assumption.