'There are already North Americans who have learned to gurgle the phrase "Bataille contra Marx..."'
-Nick Land, The Thirst For Annihilation: Georges Bataille and Virulent Nihilism
It would certainly be an arduous task to set Bataille up as an alternative to Marx, though one could say, rather, that Bataille swallows Marx up into his theory of general economy (along with all sorts of phenomena usually unaccounted for in economic theory, such as human sacrifice in the Aztec civilization, or wife-bartering among Native Americans).
Bataille's theory of economy, found in his three-part work, The Accursed Share, was deduced on a plane beyond good and evil. It is more of a Nietzschean/Sadean economics than an extension of Marx, though it is certainly that too.
Not being a moral economics, however, it poses an unprecedented evaluation of redistribution which would have certainly baffled his more conventionally socialist friends and peers. Marx's evaluation of redistribution is almost entirely moral, even when it doesn't set out to be: capital is turned over to the workers and all class hierarchy done away with.
For Bataille, revolution is simply one way of dealing with surplus. He goes entirely against contemporary scarcity narratives and posits that the flow of life fundamentally produces a far more abundant degree of resources than what could ever be used up, but only intermittently. It is then necessary to lavishly use up what is left or it goes to waste.
In the case of the Bolshevik revolution, the surplus was the monarchy itself. We deal here with a common historical contingency in which the surplus is maintained by a minority of people who have the most social power. As they have a monopoly on both the means of production and the means of squandering, the revolution acts as the squandering of lives, paradoxically, to free up the share not put to use by the working class. For Bataille, whether or not this worked in the favor of the proletariat is not a matter of concern; he simply describes this situation and re-configures it over and over to different degrees of intensity throughout history.
The gift has its origins here. The gift comes not only from an acknowledgement of surplus resources, but from the radical affirmation of the reciprocal play of forces which supposes that if something which would otherwise be squandered is given away freely, something might be received in kind. The gift is related, if remotely, to revolution. It is its non-violent counter-part.
I'm simplifying Bataille here, but who doesn't? His readers can be excused to some degree for offering conclusions since he, by nature, refused to provide any.