Interesting angle alright.. Might stump up the couple of quid for the ebook. That said, on first glance?
While I would be first to agree that the current fashion for a bloke who just needs a shave, I have a couple of problems with his reconstruction. Numero Uno; The "apelike" face. Flat nose, jutting lower face, black skinned. The nose the most obvious and provable one. For all his well thought out theory(and it is) he made one
big mistake, or loves his theory so much sought to tweak the results. The skull he picked for the reconstruction is missing the nose bone. In reality they have the dubious distinction of having the biggest conks of any human species so far discovered. We're talking Cyrano de Bergerac here. You can see this in the pic I link above comparing our two species. They had huge projecting noses.
Not even remotely like the great apes. Jutting lower face? It's how you angle the skull. Bit of sleight of hand here. Again to fit his theory IMHO. If you took a modern flat of face human and angled the head back the jaws would stick out. If you show them at the proper angle no such jutting is shown. The linked pic above shows this and here's another;

Yes they still have more of a muzzle than us and the receding chin which exaggerates this, but not nearly to the degree shown in his reconstruction.
His contention that the eye level is radically different? Same again. Squeezing the evidence to back up his theory.
Look what happens when you put them eye level to eye level;

Doesn't look so radically different now. Again the skull he picked(La Ferrassie 1 Here's his actual skull
http://www.modernhumanorigins.net/laferrassie1.html) as well as missing the nose bone was a bit of a narrow lantern faced lad. The Sarah Jessica Parker of his gang. The rest so far found aren't. Plus even here he's hyped up a bit. His forehead wasn't that low. Here's an "average" Neandertal lad compared to a modern human;

Check out the hooter on the lad on the left(the lad on the right could sue me if I get too descriptive of his own roman nose

)
Then we get to black skin. Nope again. The Ku Klux Klan would have welcomed them with open arms. As well as being red haired every so often, they were also white skinned. This is shown in the genes. They have the same adaptation as white Europeans. Indeed I'd have the notion that this is where those of us reading who are palefaces may have gotten this adaptation so rapidly. Why? The climate arguments don't quite work for me. Tasmanians who lived at similar (southern) latitudes and who were in those latitudes for nigh on 40,000 years never lost their African colouring under similar selection pressures. So white skin happening in Europe seems odd. Asian folks lost the dark skin but in a different way.
The rest of the body? Ok yes they were significantly more muscled and robust, but so were we at the time. Not up to their standards but higher than today. He exaggerates the lack of waist. I'm sure if Neandertal lad fell in with the wrong gym crowd and took up chugging anabolics he might look like that, but naturally? I seriously doubt it. The calf attachments alone show someone with little knowledge of human anatomy. Here's a comparison with a modern(though for me the height disparity is a little too much)
Yes they have a bigger rib cage, but don't walk like John Wayne, nor is their head tipped that far forward. It's more forward than ours, but not to that degree. The vertical pupils? No. No way IMH. No other great ape has this adaptation. I can't even think of a monkey that does. I seriously doubt it. Outside the film of the book anyway, for cinematic effect.
I would go along with the wolves with knives description though.