6 years Shaco main and Singed enthusiast (aka asshole) here.
What has been said is only part of what truly BM'ing is.
Quite a few people get tilted if you spam Laugh or Mastery, but many more others don't.
What is tilting is the play pattern that they offer.
Do a gank, take 1/2 of somone's hp + their flash or other summoner. Go to a bush and as soon as they push gank again. BOOM. You got a kill/forced a recall and most likely got that laner rather pissed about being double ganked. As soon as they get back to lane (all the sweeter if they don't have TP), gank them again. You don't even need to kill them, just chunk them hard so your laner can zone. That one player is now pissed at you. That player is now much more likely to overextend to try and kill you during the rest of the game.
Sure, there is likely a gold lead gained, but it's not the point. At least not to a player who chose to main such a champion.
Same happens with Singed. Enemy picks a lane bully, Singed invalidades their pick by proxying. Not only that, but with Rylai's perma slow+mov speed buff from Ult and Ghost+Defensive steroids from ult the Singed player can easily make someone waste important CDs on what looked like a sure kill only to see him walking away at 20% hp. And that's when people chase Singed and he gets to do the most out of his kit.
You don't play those champions because you want an Assassin in your comp or a mobile tanky damage dealer, you play them because you enjoy messing around with people.
Hell, my favorite memory with Shaco in over 400 games is having 3 people following me for about 6 full minutes and crossing the whole map multiple times and even having their Morgana flashing on me TWICE during the chase.