Lenin is referring not only to small business but basically to the peasantry. Advanced industrialized countries really don't have a peasant problem anymore (in this sense China is far from a really advanced country despite it phenomenal economic advances) but they do have small businesses and workers who own property (houses primarily) and/or are self-employed giving them a stake in the current economic system which Marxists seek to replace.
To overcome all this the workers need a party of their own with the "strictest centralisation and discipline." Without a Marxist party of this type the working class cannot carry out its PRINCIPAL ROLE and mission which is ORGANISATIONAL -- i.e., creating the necessary structures for the creation of socialism and educating the masses to that end.
I must admit, looking at the conditions we have today it seems almost impossible to meet the requirements set by Lenin to carry on a successful revolution against capitalism. "The force of habit," he writes, " in millions and tens of millions is a most formidable force. Without a party of iron that has been tempered in the struggle, a party enjoying the confidence of all honest people in the class in question [the working class] , a party capable of watching and influencing the mood of the masses, such a struggle cannot be waged successfully." Anyone who weakens such a party, or questions its "iron will" (or doesn't lead in its formation one might add) is objectively an ally of the bourgeoisie and against the working people.
Where do we find such a party today? In the entire Western Hemisphere only the Cuban party comes to mind. There are other parties, of course, earnestly strugglingto become such parties in different countries of the hemisphere and we can only hope they achieve the confidence of the workers Lenin seems to require. The Eastern Hemisphere shows mixed results and I have no wish to try and judge which ones are doing what. But it should be noted that the movement contra austerity in some European countries may excellerate the creation of such parties where they do not yet exist and reinforce already existing militant parties.