The stupid thing about that tagline is Kratos is a demigod either way...so it isn't even right, haha.
Characters bringing pain upon themselves is a key element of tragedy. Kratos isn't the best realized character, necessarily, but the fact that his stubbornness and inability to take responsibility cause all his problems isn't a good reason to call him a "bad character."
Also, Walter White in Breaking Bad and Don Draper in Mad Men are responsible for a great deal of their own suffering and they're some of the best characters on TV.
Well, when 2 of the 3 games is Kratos yelling about a betrayal that never happened, it's more like what Generic just mentioned above. The games seemingly wanted you to be on Kratos' side, but I really didn't care what happened to him.
I'm aware of it being a key element of a tragedy, and I think GoW1 set it up decently enough with him being the one to kill his family. His own hand causes the issue, but it does so in a way people can understand(family loss), and he has some merit to actually want vengeance. But when it comes to 2 onward, the main hook is Kratos grossly abuses his power, is warned many times about it, and as punishment loses his power. That isn't tragic or relatable, that's him being dumb. Then he calls it a betrayal and wants vengeance, when it wasn't, which is more stupidity and further, not relatable or sympathetic. Then it pretty much keeps escalating from there.
While I haven't watched much of the shows you mentioned (I know, I know), I love a good tragic character. From what little I know of Breaking Bad, Walter still had good intentions originally, so he has a sympathetic quality. When he gets screwed over, it's something he has coming and it isn't something he denies. There's more complexities to him already just from that compared to Kratos, who is one note blaming everyone for everything. I may be off base with BB specifically, but still.