I've done desk jobs all my life, including 17 years in IT. My parents never understood what I do either, yet they are understanding. My father, despite being a manual worker, encouraged me to go into IT because it was an emerging field and he didn't want me to work as hard as he had to.
So there isn't necessarily a direct link between your parents not understanding your work, and not understanding why it is tiring. And that is probably a good thing, because you'll likely never get them to understand IT.
Rather than try to show them how a mentally draining job can leave you too tired for mowing the lawn, try to flip it around, and show them that too much manual work will leave you too tired to concentrate on your job!
Perhaps say something like:
You may not believe me when I say my job is tiring, but it is. And after I mowed the lawn for you last night and did my night time job I could barely concentrate during the day. Do you want me to lose my job because I'm too tired to think straight?
Obviously, I'm not encouraging you to dodge chores. Because when you get your own place you'll have a lot more to do after work than just mow the lawn and tidy one room. But if your parents are heaping unreasonable chores on you because they think some fresh air / hard manual work will do you good after work, then this may be the way to go.
Our generation may never have to physically work as hard as our parents / grandparents did. That's progress for you. But our generation also has more reported cases of stress, anxiety, burnout, depression and chronic fatigue disorders too. Older folk who tell us we have it easy often forget this, that is if they even believe all those things are real.
Don't use the information in that last paragraph to guilt your parents into leaving you alone, but you could use it as the basis for a frank discussion with them. Otherwise, just try to work out this problem from within yourself - remind yourself that you don't want to fall to anxiety and burnout, so don't let your parents or anybody else stress you out.