Your selection of exercises looks good. I would further categorize them like this:
Deadlifts (2 work sets of 4 reps) - hamstring-centric
Press (3 work sets of 5) - upper vertical push
Ring Dips (3 work sets of 9) - upper horizontal push
1-Legged Squats (3 work sets of 7) - quad-centric
Pull Ups/Chin Ups (3 work sets of 8-10) - upper vertical pull
Inverted Rows (3 work sets of 8-10) - upper horizontal pull
Dumbbell Bench Press (3 work sets of 6-8) - upper horizontal push
So looking at that, first glance shows a classic error in prioritizing push over pull. I'd balance out your pushing with pulling. Perhaps eliminate the extra horizontal push, or add another horizontal pull to counterbalance it.
There are plenty ways to split it, but typically you'll want to have sufficient time between workouts. A few common splits are legs (quad/hamstring), push, and pull. You could also do legs, horizontal push/pull, vertical push/pull. If you only have two workouts, do something like dead-lift and upper pull, then squat and upper push.
You noted this is strength/hypertrophy training, however those are two different goals. You can gain strength without necessarily gaining muscle mass simply by improving your neurological efficiency. In fact, the most common response to training is strength which is why building muscle is so hard. Strength training will typically focus on generating as much force as possible, so either heavy reps (high mass, slower acceleration), or moderate reps with higher acceleration (i.e. speed). If hypertrophy is your goal, then increasing load and changing exercises should be your focus. You might consider something like Hypertrophy-Specific Training (HST) and consider swapping out your exercises for new ones every few sessions.
The two guidelines I typically use for changing exercises is either plateau (i.e. the first time you can no longer add weight and hit your rep target, then it's time to change the training) or frequency (i.e. every 3rd or 4th workout - 3 is good number because the first workout you learn the exercise, the 2nd you are comfortable with it and the 3rd you can then push past the previous load before moving onto something new).
The frequency during the week looks fine. I would never train with weights more than two or three consecutive days without having a day with either full rest or a different activity like cardio. I know some people like to train daily with splits but every workout taxes the central nervous system and it needs to rest and recharge as well.
Best of success with your training!