Private ownership and the protection of those property rights are exactly what capitalism is. As long as there is no coercive entity dictating what YC can and cannot do with it's capital then HN absolutely is a product of capitalism.
Capitalism doesn't mean "earn[ing] enough through its service to support itself". Why do you think that people are not free to finance sites that promote other branches of their business under capitalism?
Capitalism doesn't mean "earn[ing] enough through its service to support itself". Why do you think that people are not free to finance sites that promote other branches of their business under capitalism?