This is an exceptional idea. The modern first-world lifestyle is, at heart, an overabundance of everything. Which is a great problem to have! And yet the 24 hours in each day have not expanded to accommodate all of the available options. If you try to chase all of the things that seem either necessary or desirable, you will slice and dice your life into far too many teensy segments, leaving you scattered and thus unable to either do all of the "must-dos" well or to actually enjoy the "wanna-dos" to the degree you'd like.
I'm going to recommend for you an exercise that worked for me; obviously, YMMV. First, list your priorities. Then, for a week, track how you spend your time. When the week is done, compare the two things. Where there is a disconnect -- where you are spending lots of time on something that isn't on your priority list -- figure out why you're doing that.
Note that the standard advice is just stop doing the things that aren't on your priority list. And that is the ultimate goal. But sometimes, the problem is that your priority list is incomplete. So the first step is to check your work and complete the list.
Sometimes, you will find the disconnect is due to a priority that you had not put on the list. Like, for example, your largest chunk of time will likely be at work. Now, you have topped your list with being a better dad/husband (just like mine was being a good mom and wife). For me, I felt guilty about looking at the hours at work, because it was taking away from what I said was my top priority. But then I realized that "supporting my family" and "saving for retirement" and "saving for college" were also very high priorities; I just wasn't considering them. The significant time you spend at work is actually serving the very high priority of not living under a park bench, so put those priorities on the list and give yourself credit for the time you put into them.
Sometimes, you will find that the disconnect comes from a need that you haven't voiced. For example, I did this because I was frustrated that I was frittering away way too much time on the internet instead of getting my work done -- like, I kept saying my family was my priority, but I just spent two hours putzing on the web, so I'd have to stay later to make those hours up, so what a terrible person I was! When I really scrutinized how I spent my time, though, I realized that my whole life was filled with meeting others' needs -- I had two young kids, a husband, a house, and a job that was basically solving other people's problems. I went from hours at work dealing with client demands, and then the minute I pulled up at daycare, I had a very-ADHD-6-yr-old and a 2-yr-old to manage, and then once they went to bed, I had house stuff and errands. I am an introvert and need significant downtime, but I didn't have any time for that built into my day. So when it had a chance -- like, when I could walk into my office and close the door -- my brain would just shut down and take the time it needed.
Now, the funny thing was, I had never aspired to be the mom who cut her kids' sandwiches into pumpkins on Halloween, and yet I had still spent most of my life since my DD arrived trying to be That Person who could go 24/7 and juggle 8000 things -- and then feeling guilty when I couldn't achieve it. But no matter how much I want to be That Person, I'm not. And that means my choices are to spend the rest of my life berating myself for not being someone else, or figure out how to work with the who I am. When I said it that way, I realized how incredibly stupid it all sounded and decided option 2 was the better approach. So I instead gave myself permission to just shut off for an hour or two each night, regardless of whatever other chores needed to be done. For you, I wonder if something like gaming falls into that category -- if it's something you really enjoy, if it serves some sort of need inside you. Taking care of yourself is also a priority. So if gaming falls into that category for you, rather than trying to be someone else's version of a perfect you, give yourself permission to make time for that in your day. [And make sure your spouse does the same!]
The way you do that is to be absolutely ruthless with all the crap that doesn't fit into your priority list. Anything that is on the list because it is something that "should" be done gets whacked. "Should" means it's not something you care about, but something you're doing to meet someone else's expectations. If that "someone else" is not your spouse, then it doesn't matter, and you shouldn't spend one more minute worrying about it. The day I gave myself permission to never attend another PTA meeting was absolutely freeing.
Then, for the things that need to be done but you don't like, figure out what minimum level is "good enough." Like, my yard will never be in Better Homes and Gardens, because I am not good at growing things, nor do I enjoy that. OK, minimum standard is lawn mowed and weeds not taking over entirely -- done. Then figure out how you can achieve that minimum required level with the least impact on your priority list. Start with the things you hate the most. For me, that is housework. Cooking is fine -- it's a big chore when you've got to do it every night for 4 people, but I do enjoy cooking in general -- but mopping floors and cleaning toilets? NFW. So I decided to focus my minimal housekeeping skills on the food side of things -- menu planning and cooking on the weekends to prepare for the week -- and outsourced the cleaning.* And I also had a couple of default standbys in the fridge/freezer for days when takeout sang its siren song.
Note that this is going to be an iterative process. You won't get everything right the first time. You'll definitely have to develop a thick skin to resist the guilt/pressure from all the people who want you to do those "shoulds." And over time, the "must-dos" and "wanna-dos" will change, particularly as your kids grow. But the nice thing is that if the choices you have made until now no longer fit at some point, you just re-evaluate and make a different choice. Honestly, for me, sometimes just re-doing the exercise reminded me that where I was continued to be the best balance across all of those priorities. There's no perfect, but being thoughtful and analytical can help focus your life on the things that are more satisfying.
*Yes, FI was a major goal, so I considered it in making that decision -- I did the math and figured out how much longer I'd need to work in order to continue employing cleaners every other week, then I decided it was absolutely worth it to work that much longer never to have to worry about that again. Really, my level of hatred for cleaning cannot be overstated.