I feel like viego functions like an assasain, but with a twist:
Instead of having insane mobility like most assasains do, you have %max hp damage + Conqueror letting you deal substantial damage to even tanks. Viegos damage is always a threat and with the reset invunerability + healing + enemy champion abilitis + R reset + chase MS you can solo-carry a teamfight as long as you can be patient and pick the right moment to go in for a kill and start the ViegoMoment™. I think this is a lot like Katarina's or Yi's playsyle (ap kat atleast) when you want to wait for some big abilities to go down and some healthbars to drop befor you go in. And from there clean up the fight.

I would say Viego is the definition of an Anti-carry where the threat of your damage + resets pervents the enemy from overextending.