I would like to know what their replacement for free market capitalism is, as the description is entirely hand-waving. I hope it's not some sort of socialist or communist utopia as those are disastrous in practice.
There's really nothing outdated about capitalism. It's the political systems that are outdated, where they can't control the ever-growing capitalistic protocol and give it inputs to produce desired outputs. Or anything else for that matter. Voters are too stupid to understand anything complex, and they elect politicans who have no clue or care for it either. And it's been like that pretty much since forever. It's just that last few centuries the technological progress was so powerful that it was able to overcome even the most radical political attempts at ruining everything.
Unfortunately politics are a hard coordination problem - trying to make robust global system out of pieces who have incomplete information, are flawed, irrational and often actively malicious. Distributed systems are hard even assuming near perfect conditions and trustworthy agents, and with such conditions and requirements - it might be unsolvable problem.