Is he like the Anti-melee hero god? He deals absurds amount of damage to melee heroes

Played shaco, Got decimated in about 2 seconds with wits end and madreds, only had a rylais, and ninjatabi. Flamespitter dealt around 400, ultimate dealt around 500. Ultimate deals more than veigar's if your in it for 2 seconds.

words of advice
fear with box, get behind him, hallucinate + your madreds, don't stand in his ult

Silences, slows, stuns, disables etc are your friend against Rumble.

At the end of the day, Rumble is 80+% magic damage. If you don't take any magic resist gear, he hurts a lot.

As for dealing with Rumble's ult, the best advice is to get out of the way when the rockets fall because the damage over time on them is painful, and slowing. Just remember it is a huge skillshot.

If he is melting you that fast that means he has decent to good AP. More than just a rylais or it's end game and everything is ranked up. I've played nothing but rumble since the patch. Proly has runes/masteries too.

Pro tip though: If he is melting you that fast that means that he himself is squishy. You could likely do the same exact 2 second kill to him. Caveat being if he has spell vamp and is able to get off electro harpoons before dying. Or my personal favorite: spell vamped smite + spell vamped spell blade .