The first author E mentions as a presumed contrast to Shakespeare is Marlowe, so I assume E accepts Marlowe's authorship of the plays and poems we know as his. Let's take a look at the evidence. There are no manuscripts of Marlowe's plays, no letters written by him or to him, in fact no examples of his handwriting at all except a signature as witness to a will in Canterbury in 1585, when he was 21 years old, spelled "Christofer Marley." Not once during his lifetime was he ever referred to as a playwright or poet; surviving references spell his name every way from "Marly" to "Marlin," but almost never "Marlowe." The name "Christopher Marlowe," in any of its spellings, was never associated with any play or poem or literary work during the man's lifetime. There is no evidence to connect him with any acting company, or with the theater in any way. The only play now generally attributed to Marlowe which was printed during his lifetime was Tamburlaine, but it was printed anonymously in 1590, and was not attributed to Marlowe until 1671 (no, that's not a typo), 78 years after the man's death. In 1594, the year after "Marley" (as he himself spelled it) was murdered under shady circumstances, quartos of two plays --- Dido Queen of Carthage and Edward II --- were published with the names "Christopher Marlowe" and "Chri. Marlow" (respectively) on their title pages; this was the first time the name had appeared in any literary context, but (at least by Oxfordian standards) there is nothing to connect it with the recently-murdered shoemaker's son from Canterbury. Out of E of O's list of things that "suggest a literary life," only one applies to Marlowe: we have a record of his education, since he (supposedly) went to Cambridge. But if I wanted to play the Oxfordian game, I could easily challege the evidence for that: most of the Cambridge records which are supposed to be to the shoemaker's son spell the name "Marlin," and there was another student there at the same time named Christopher Marley, so those references could be to him; also, what was "Marley" doing in Canterbury to sign that will in 1585, when he was supposedly at Cambridge? Anyone who accepts that Christopher Marlowe wrote plays but refuses to accept that William Shakespeare wrote plays is applying a double standard of the most monumental proportions.
Marlowe is probably the most extreme case, but I could go on at length about other contemporary playwrights. E of O is upset that there is no record of Shakespeare's education (though the circumstantial evidence for his attendance at Stratford Grammar School is very strong), but the list of other Elizabethan poets and playwrights for whom there is also no educational record is a distinguished one: Ben Jonson (considered the greatest classical scholar in England), Michael Drayton (one of England's most popular poets, mentioned by Francis Meres in Palladis Tamia more times than Shakespeare), George Chapman (translator of Homer, also a great classical scholar), John Webster, Thomas Dekker, and many others. There are others, such as John Fletcher and Thomas Heywood, for whom the evidence of schooling does not meet Oxfordian standards of proof, so we can add them too, if we're going to play by Oxfordian rules.
As for other kinds of evidence, many of the most prominent playwrights of the day have left us astonishingly little evidence of their lives and activities. The Duchess of Malfi and The White Devil are two of the greatest Jacobean tragedies, both still performed today; they were attributed at the time to "John Webster," but this name was not convincingly attached to a real-life person until 1976, when Mary Edmond showed that the dramatist was almost certainly the son of a coachmaker also named John Webster. Even so, we don't know exactly when John Webster was born (1580 is our best guess), where he went to school (the Merchant Taylors School is a guess), or when he died (it could have been any time from 1625 to 1634); essentially no personal information is known about him. Then there's John Fletcher, one of the most popular and famous Jacobean playwrights (at the time), part of the famous team of Beaumont and Fletcher. Large chunks of his life are completely unaccounted for, including the period when he supposedly started writing plays; we know nothing about the last ten years of his life; we don't know for sure if he was married; there are no autograph manuscripts of his plays (though there are some transcripts in other hands), and only a single signature; his name appeared on title pages of four plays during his lifetime, but 22 years after his death a massive folio attributed dozens more plays to him and Beaumont.
Back to William Shakespeare. E of O seems genuinely puzzled when he asks where there is any record linking the man with the works. Well, for one thing, his name appeared on the title pages of many plays during his lifetime, plays which were performed by the acting company of which he was a member. A man's name on the title page of a published work seems to me to be evidence that he wrote the work in question, or at the very least, evidence that people thought he wrote the work. It's true that Shakespeare's name appeared on a couple of plays (The London Prodigal and A Yorkshire Tragedy) which are universally agreed not to be his, because they are markedly inferior to his work and do not appear in the First Folio; that just means that his name was a selling point, and does not affect the fact that the publishers of these plays were asserting that he wrote them. Of course, there's the First Folio, with its commendatory poems and testimony from Shakespeare's fellows Heminge and Condell, which Oxfordians are forced to dismiss as a hoax. There is nothing about the First Folio to suggest it is a hoax; I don't feel like arguing against all the standard Oxfordian assertions right now, but I'm prepared to do so in the future. There's also the monument to Shakespeare in Holy Trinity Church in Stratford. Oxfordians also dismiss this as a hoax, as of course their theory requires them to; they claim that the monument originally showed Shakespeare holding a sack of grain and that it was later altered by conspirators, a scenario I am more than prepared to argue is ludicrous. Aside from all this, there are also numerous references to William Shakespeare during his lifetime, including third-person references and poems addressed to him. Oxfordians claim that these references do not identify Shakespeare as a person, which is not true; several of them identify him as an actor (the Parnassus Plays, John Davies' epigram), and/or as unlearned (Francis Beaumont's poem). (I am fully aware of Oxfordian attempts to explain away this evidence, and will glady get into specifics when time permits.) John Davies' epigram, written in 1611, was manifestly addressed to William Shakespeare, the actor in the King's men, and certainly not to the Earl of Oxford; I'll argue this point in detail if need be. When Edmund Howes made a list of modern poets in 1615, he scrupulously listed them according to social rank (knight, esquire, gentleman, or none of the above), and Shakespeare was listed as a gentleman, which in fact Shakespeare of Stratford was.