I think it is the fairly broad sociological definition of globalization actually, no matter what political camp.

To cheaply use Wikipedia as a reference: "Globalization or globalisation is the process of international integration arising from the interchange of world views, products, ideas, and other aspects of culture."

I do not see how this is necessarily capitalist. What you mention as internationalism sounds more political and economic than globalism does, whereas I think of globalism mostly in terms of culture.

Certainly, the cultural spread may be crass American consumer culture in many cases, but it is also far more than that. Modern technology and political institutions allow us to easily communicate and travel in a way people could not even dream of in the past, which narrows the distance between nations, spreads culture and forms previously unlikely thought bonds between humans. When viewed in this way, I do not think globalism becomes irrelevant as a term even in a socialist world.