At 8, 4, and 3 they probably play well together and really should be doing so as often as they can. Participating when they ask is pretty good but it's also good that they see that you like things yourself and have interests of your own.
You can also separate the concept of everyday activity with special occasions. Sure, by the day to day you may be found watching things, playing video games or whatever. But for me, summer time means go do something while school is out. We take them to the beach, amusement parks, rock climbing, etc. And those experiences and the unavoidable family interaction within them tends to be the lasting memories and impressions.
I think so long as you are sane, happy, and occasionally adventurous, you are doing a pretty good job.
If you're feeling some kind of guilt about your choice of pastime after work, then it might be a good idea to switch it up a little. It might not have to be as complex as learning violin though. You already know how to read, right? How about picking up a book and reading to whichever kids will listen? I read the Hobbit to my 3 year old and she was pretty into it. That was a segue into other classics as well. That lead to a desire to be odd characters for Halloween instead of princesses and ramped into unconventional costumes that I had to make because nobody sells them, and a desire to write horror stories over the course of a few years. All of which made me more engaging and I definitely feel better about my own involvement even though I too play a lot of video games (some with them) watch TV, etc. Sometimes I just plain fall asleep on the couch after work. But I feel I am doing ok as a parent in spite of my own laziness.
I say keep it up, but make sure you are happy yourself. Bettering yourself doesn't have to be a monumental challenge. Or even a change in anything but perspective.