His winrate even for top in Plat+ (champion.gg) is only 51%. Broken is an extreme word to use but he's basically like an Annie. If you're in his range when he's close to supercharged and with ult., you'll get shredded and snared more than once due to how his CDs work. On the other hand, he does have a short range, lacks mobility, is very mana hungry and needs scaling items. He's also mostly single-target focused, light on the CC (overall much less than Mao etc.) and isn't really capable of initiating or providing a frontline. Most top-laners, such as Hecarim, are able to initiate and dive the back-line. Also, despite people's claims that Ryze is a late game champion, I think he's strongest early-mid game where it's mostly skirmishes. He is amazing in 3v3s but far less so in 5v5. In fact, his winrate drops to 48% as Top when games go past the 40 minute mark in Plat+.
These are the facts from a balanced point of view. With that said, laning vs him is very frustrating. When he is "ready to go" with a high mana bar, his passive and his ult., he is among the very best duelists in the game if not actually the best. The picks I've seen work best are Wu'Kong, Irelia, Hecarim, Rengar, Anivia, Akali, Mao (not as bad as the LCS game suggested), Renekton, Fiora and Vlad. Anivia can abuse Ryze's short range while being more impactful in teamfights and not particularly easy to burst. She can control the lane enough that Ryze will basically never get a chance to do anything. Fiora and Wu'Kong have very high damage while being able to "dodge" Ryze's passive with their own ults. if timed properly. Irelia's tenacity also works great against Ryze since the W is less impactful and yet she also has high burst.
Is he overpowered? I'm not actually sure but I'd lean towards "Yes" because I think his early damage is a bit too much. On the other hand, people don't see him much and don't respect his stacks or range. I think this is in part Riot's fault since the stacks show up the same blue color instead of being something more easily identifiable like red (suggesting danger).