In Marx’s day there was no such thing really as a capitalist service sector. Service workers were invariably people who offered their services directly on the market, not as the employees of capitalists who profited from provision of their service. Consequently, Marx writes about the “service sector” in this sense:
"The pay of the common soldier is also reduced to a minimum — determined purely by the production costs necessary to procure him. But he exchanges the performance of his services not for capital, but for the revenue of the state"
"In bourgeois society itself, all exchange of personal services for revenue — including labour for personal consumption, cooking, sewing etc., garden work etc., up to and including all of the unproductive classes, civil servants, physicians, lawyers, scholars etc. — belongs under this rubric, within this category. All menial servants etc. By means of their services — often coerced — all these workers, from the least to the highest, obtain for themselves a share of the surplus product, of the capitalist’s revenue.
"But it does not occur to anyone to think that by means of the exchange of his revenue for such services, i.e. through private consumption, the capitalist posits himself as capitalist. Rather, he thereby spends the fruits of his capital. It does not change the nature of the relation that the proportions in which revenue is exchanged for this kind of living labour are themselves determined by the general laws of production."
Things like the service sector are important to Baudrillard, who wants to talk about how the new service, the new simulation has taken over and completely replaced production. The service sector is the new economy and there is no more production. The purchasing of these services doesn't make one a capitalist, Marx says. But this just means he's spending his money, the fruits of his capital, on services.
However, Marx doesn't seem to consider the possibility that one such capitalist will make the services offered into a business, and invest in the capital and labor necessary to commodify, socialize, professionalize, those services.
Marx only considers the service industry with respect to the exchange of goods for labor. But there is a whole industry to develop from this idea, whereby labor is exchanged for labor, and enormous profits to be gained.