That is a solid plan, and worth it to follow. That said, just about ANYTHING you do in the gym is going to translate on the court, guaranteed.
This might be a personal preference but a few tweaks I would make are:
Legs:
Skip the extension and press machine and opt for Squats instead. If you do feel like blasting those quads then the leg press is your friend! The importance of legs is not in the front (quads) but back (hamstrings and glutes) which is why I like deadlifts for tennis players.
Also
Kettlebell swings, can't stress those enough i forget where the quote came from but "If you're an athlete, in any sport, this will make you better at it" and its as true as it gets. Great fast paced cardio/strength movement that exaggerates the hip snap and gets your hamstrings, glutes and core all working together. You can also do so many other things with KettleBells that make them a serious tennis players best friend (Deadlift, pop squat, goblet squat,
turkish get ups, clean and press, etc)
Monster walks is my preferred alternative to the hip abduction/adduction machine
for obvious reasons. I have a long band so i usually wrap it around a pole and walk backwards until its fully stretched out then slowly walk back and repeat. Great warm up exercise right there.
Core:
Skip the crunches, do planks instead (get the back core working too). There are
so many ways to do planks and they're much more effective. My personal favorite is the
Plank Row.
I've recently been hyped to
Vertical Core Training and I love it! Many ways to progress and it works your core in a far more practical manner.
Finally once you see the
Half-Kneeling anti rotational chop...well no explanation really needed for a tennis player. I also prefer to do these with the rope instead of a bar, and you can also do them just laterally instead of low to high, great core exercise!
Shoulders
Solid plan they have in place, can't stress enough the importance of strong shoulders to protect the rotator cuff.
Eric Cressey is the guy to learn from for shoulder work. He works with a lot of overhead athletes (Baseball, quarterbacks, etc, tennis players are no different) and quite frankly I'm a huge fan of the bottoms up KB press and Landmine press.
Check out the
Overhead Shrug for a great alternative to a standard shrug, and the video displays it's benefits over the standard shrug.
Arms and Back
Great progressions, but as tennis players, Left/Right imbalance comes into play and i can't stress enough the importance of dumbell work here to ensure both arms are lifting equal weight. This is helpful with bicep curls, tricep extensions, and
single-arm rows and chest press just to name a few.
I like the lat pull down, but IMO once you can start doing pull-ups for reps then start doing those instead. Then again, I want to be good at pull-ups so our goals may vary. I have noticed i hit far better volleys after doing pull-ups.
Don't forget to stretch and foam roll. Equally, if not more important than the training itself.
Hope that helps...man, I should consider becoming a trainer