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Nope, not the Shakespeare play but a prose adaptation that's sometimes considered the first novelization of another work (which seems an odd choice to anybody familiar with that peculiar play). Broadly speaking a novelization since this Wilkins work isn't long enough by our standards to be a novel and is really more a very lengthy synopsis. Still it was sold separately for an audience that apparently wanted such a thing, who perhaps couldn't make it out to what was a very popular play at the time. (It was one of the first, if not the first, Shakespeare play staged after the Restoration.)
The more important interest though is the relation to the play. Most, but not all, scholars believe the play was co-written, some even identifying Shakespeare's contribution to about half the finished work (typically acts 3, 4 and 5). For a time some even thought the play was adapted from this book but it's now widely considered to have come first. The play itself is a mystery - did Shakespeare actually collaborate with somebody, did he adapt or revise a pre-existing play, did somebody else revise a full Shakespeare play? It's no help that the existing text is notoriously corrupt - imagine what our opinion of Hamlet would be if all we had was the First Quarto. (One possibility that I haven't seen mentioned is that the publishers of the play simply added the first two acts on their own, more plausible if you consider the existing text of Pericles as a memorial reconstruction in which case the early parts might have been missing or considered too slight.)
Wilkins is one of those shadowy Elizabethan figures remembered only by connection to a literary work much like, say, Cyril Tourneur. He owned an inn (which might have doubled as a brothel), was in frequent trouble with the law, wrote at least one other play and was apparently a violent person. He's often identified as the author of the play's first two acts purely because of this novel, his one other (known) play, and because he knew Shakespeare (they were both witnesses in a 1612 trial).
The linked book is an 1857 edition that includes much background material and a comparison of the novel and play. The editor Tycho Mommsen was Theodor Mommsen's brother and a buddy of Theodor Storm. Tycho in fact was the first person to suggest that the Hamlet Q1 was reconstructed from memory. He later produced a critical edition of Pindar and was a specialist in Greek prepositions (well, probably somebody has to be).