BI is certainly the type of thing many actual.socialists have proposed, and the definition of socialism you post is, while perhaps what made ght be found in a particularly compact general dictionaries, not particularly accurate or complete, even by the standard of general dictionary definitions.
Google's is pretty typical of not-unusually-compact general dictionary definitions, "a political and economic theory of social organization that advocates that the means of production, distribution, and exchange should be owned or regulated by the community as a whole."
Unlike yours, it encompasses regulation (which redistributive taxation is generally recognized as a form of) and the focus is on "the community as a whole" (for which the state may be the tool used, or may not) and not just the "the state" as the focus (which is important, since without that it wouldn't include libertarian socialism.)
