All unrighteousness is sin. I've never called boredom a sin, but I do think it's pretty deplorable. I don't think very highly of people who frequently say that they're bored. Maybe I'm just really closeminded about it. To me, there's ALWAYS something to do, so I just don't understand boredom. Plus, my mind is always moving, so I could be biased.
I just don't get it though. Read a book, paint something, clean something, rearrange furniture, memorize scripture, pray, go visit someone, write a letter, take a walk, play a game, visit a friend, bake bread, cook a meal, clean out the fridge or garage, go to the gym, teach yourself a new hobby. There's just ALWAYS something to do. I truly don't understand boredom.
But is it a sin? I think that's a stretch.