Ok I can't remember off the top of my head, but are you keeping the sets the same on the lifts you noted on days 3 and 4? Or is that in the program?
Also, are you not hitting abs and calves like it says? I would.
I'll go day by day:
Day 1: Looks good, though personally I would just do high rep band pull-aparts or some shoulder rehab stuff pre-WO instead of the rear delt flies everyday. Also, why HS rows as opposed to something like DB Rows?
Day 2: I would personally do a Squat variation. The whole principle of the book is to do big, compound movements that ideally have you moving your body through space. Also, traps aren't hit in this program directly, so I would drop the shrugs. Do calves/abs
Day 3: Would do a SLDL or a variation for hamstrings/legs. And I would do a vertical pull, like chins or pulldowns for back.
Day 4: Would do Squats again.
I suggest the Big lifts you want to increase, like Bench, Squats, OHP, do once on high rep day, then repeat on low rep day. So you get a lot of 'practice' with them.
Also, do you have the ebook? If not, find it and read it. You want BIG, COMPOUND movements. Only time I used machines/cables were usually for small BP's like arms, calves, rear delts, etc. Machines for Legs and Back movements are likely not going to be great.
Personally, I would do something like this:
Day 1: Weighted Chins
BB Bench Variation
Calve Raise variation
Day 2: OHP variation
Day 3: DB Rows
DB Bench variation
Tricep Compound (CGBP, Dips, CG Floor Press)
Day 4: Same lifts from Days 1 & 2
This is all opinion, but this what I would do, and only make adjustments after at least going through a 6-week cycle of the program.