He's talking about Marx's actual definition.
https://en.wikipedia.org/wiki/Socialist_mode_of_productionThe core principle of this is stated as " to each according to his contribution". Which effectively means that the value of your input = the value of your remuneration. Which was very much at odds with early capitalism, in which the business owner gets the majority of the value that each worker creates. Basically, if
anyone other than the person who inputted the labor gets a
cut of the value you created, it fails to qualify as socialism according to Marx's written definition. That includes either private landlords, rent extracted via management, or government owners who take a slice of the action. All of those go against Marx's explicit definition: the core principle is that the value of what you created is respected. You can take value from someone who created it, but not without replacing it with something of equal value. So ... under a purist Marxist model of socialism, even taxes are disallowed, because they take value away without replacing it. The early Marxists were divided on this issue, some said no taxes
ever while others argued that
some taxes were needed to maintain roads and the like. So ... basically a similar argument to libertarianism.
The other principle stated here is that the
working class own the means of production. That effectively means either democratic control of centralized resources, or worker owned corporations. Marx was very clear on this: dictatorships that centralize production don't count as "socialism" because they lack the "working class owns the means of production" thing. They also fail the first test, "to each according to his contribution" since those governments take value away from the workers who made it, effectively robbing them of their labor value, from a Marxist viewpoint.
Hell, if you count any type of centralized control as the only criteria, then the Roman Republic / Roman Empire and basically everything else is "socialism" rendering the term completely meaningless.