I'm actually being half serious. Because of the way lol designed its mechanics and itemization, no champion can be completely unplayable. Anyone with 400 range can buy infinity edge, crit item, last whisper, bloodthirster, and become an adc. New Veigar is not suitable for adc however, as he has no steroid and no dash/escape mechanism and no high autoattack range.
He has a trap ability to stick to/catch up to his targets and the ability to stack ap, even though he cannot use his stacked ap efficiently (effectively 60% scaling on his basic abilities... it's really abysmal--mages usually have 180%) with his skills, he can use his stacked ap with nashor's tooth and lich bane's passives. Since more ap items would be ineffective on him, and he needs to get into close range to auto or use his ult, it's only natural for him to build tank after a damage item or two. This give him the kit of an ap autoattacking bruiser.
That being said, my point was to accentuate the ridiculousness of his most optimal build, given that riot wanted to keep his identity as a burst mage.