To answer your last question: No, you should not let them decide what to do if that means doing nothing. Kids will tend toward nothing if they have the choice, and that means they will never know what might have interested them.
K., ask yourself: Is this post about getting confirmation that your kids are just fine, and you can let them decide what to do? Or are you really ready to help them navigate finding some more challenging ways to spend their time?
Yes, they do well in school and aren't any trouble. Check. That's excellent. And yes, they have played sports. Fine. And you don't want to over-schedule them.
But a couple of thoughts from a parent of a middle schooler:
Kids know what they're exposed to. Someone posted below that maybe your sons will get interested in "art or cooking or woodworking or archery" and that would be great, BUT....they won't wake up one day and say, "Mom, I think I want to learn to cook!" or "Wow, I'd like to try archery!" They don't know which end of a bow is up, or what woodworking involves. Unless you take some initiative and work with them to find some activities to try -- to taste something new and outside their comfort zones of video games and running around outside -- they will not ever know if they might have liked certain things. Kids know what WE expose them to.
They should have a big role in choosing but you need to push them to choose. City or county parks and recreation departments often have huge catalogs of courses and classes for kids these ages -- sports, yes, but also unusual sports like archery and fencing, computer programming and game programming, many kinds of arts, even orienteering (using compasses outside) and letterboxing (going into parks and forests to locate "letterboxes" by using coordinates). Get a catalog and sit down with each boy one at a time and have him pick something. These tend to be four- or six- or 10- week classes, not gigantic commitments that go on all school year long. It's a good way to taste things and get them outside that comfort zone, because frankly right now, in the name of not overscheduling them, you're letting them coast in that zone.
You post that you have made such offers and they shrug them off. I would gather up ideas, maybe even go online sitting next to them to see class catalogues etc. and be clear that this time they will pick something. They get the freedom of choosing-- hooray. YOU have the authority to say, you are going to do something, and don't get to shrug it off. It's not a lifetime commitment but you need to taste new things or you will never know if you liked them and might have continued with them. Period. If they kick up a fuss about it, can you be tough enough to paste on a smile and say, "Kiddo, if YOU find another class you want more than this one, you can try it next time around, but you're doing this for these eight weeks" or whatever?
If you can locate a positively minded friend of theirs to try something new with them, that can help a lot, but if you think the pal will only become a "misery buddy" and they will spend all the time complaining to each other, better to have your son(s) try a new thing as a new kid, so they can focus on the activity and not their pal.
Before everyone says, "But kids need down time! Let kids be kids!" yes, they should not be so scheduled that they never have a Saturday morning free, or never have a second on a weeknight to read a book for pleasure. But bear in mind: Your sons pretty much have video games and neighborhood friends. And honestly, as they get older, the neighborhood run-around thing will fade quickly as their friends get more involved in activities and as everyone gets more and more homework. And video games don't encourage them to think and move and act in real life in new ways.
I want to add that I back Ms. May when she says there's more to life than sports. Take care that team sports doesn't become the focus because there are a lot of kids who miss out on other things they might like but their parents assume that as boys, they should be doing a team sport and they're fine if they do. Break away from that mindset and have them do at least one activity that is not a team sport. Believe me, they still will not be overscheduled -- a kid doing a team sport for one season, and a class in, say, woodworking for 10 weeks, and taking fencing lessons year-long -- that's not overscheduled, not where we live.
One last thing -- your older son is nearly in, maybe already in, middle school. It can be really helpful for kids in MS and HS to have an activity that is theirs and theirs alone and is done outside school. If they get swamped by school or overwhelmed by the academic work and social pressures, they know they have that part of themselves that loves that activity. My daughter is like that with dance -- it has nothing to do with school; it is physical so it balances the huge amount of academics she has; and her friends there do not go to her school so it's an escape from talking about school. She does like school plenty; it's just also good to have a place and friends and activity where she is "the dancer" and not "the student." Something to consider.
And finally -- have your sons tried scouting? If they did and didn't like it, please be aware: Every troop is different. Some might be very outdoorsy all the time while others are more into service projects and helping others, or may combine both. It's never too late to enter scouting, and it should be varied so they do different things throughout the year. Again, something to consider.