Workdays
4:50 AM Wake up and bathroom time
6:00 AM Walk the dog
6:30 AM Breakfast and Changing for work
7:15 AM Start Commute to work
7:45 AM Work
6:00 PM Work ends, Commute to home
6:45 PM Arrive Home, help with Dinner
7:45 PM Actually eat
8:30 PM Rest
9:30 PM too tired to do anything. Browse the net
I think you need to work on doing things faster, or perhaps your time estimates are a little off. For one, if making dinner and eating it really take 1:45 each night, find ways to shorten that. My wife and I cook things in the crockpot frequently. A little prep time in the morning, we come home from work and 5-10 minutes later we are eating. We have an 18 month old daughter, we don't just wolf our food, and eating dinner takes maybe 30 minutes. Without the kid it'd be 10-15.
Also, definitely think you should sleep in and get an extra hour of sleep. Unless your job is breaking one rock with another rock (and since you bring your work home I'm guessing it's not) you shouldn't need an 8:30 rest unless you are sleep deprived.
Saturday
7 AM Wake up
8 AM breakfast
9 AM Home chores
11 AM Work at Home
12 Noon Lunch Time
2 PM Going out with family, Malls and parks, maybe movies
8 PM Time with missus, if Work-at-home permits
Sunday
8 AM wake up
9 AM Home chores
1 PM Lunch
3 PM Home chores
8 PM Continue work at home
10 PM Too tired to do shit
I get family time and work at home, but why are you spending so much time doing chores? Again, 18 month old daughter who runs around the house spreading her toys everywhere (we are teaching her the clean up game, and she's pretty good at it) and even still my wife and I don't spend collectively what you do on chores. Are you OCD? Do the floors need to be steamed every weekend?
Also, going back to the sleep deprived thing - if you are sleep deprived you probably aren't working to your greatest potential and could accomplish more during actual working hours which will help free up your weekend. A little more sleep each day could actually open up how much time you have to spend.
Lastly, being too tired to game could mean you need to shift what game you are playing. I know some games I need to be in the mood for, or have the energy for, like Bloodborne. But, if I'm dragging I can always through some Forza Horizon 2 on and not miss out on much due to low energy. Find a few low key games you can play whenever and I think you'd end up playing more.
Hope this helps, and hope you can revisit some stuff. I don't mean to sound mean, but your schedule does not leave much time for fun in your life.