Post scarcity worlds are hard to write to because most of us think in scarcity terms. Part of the fun of writing about post-scarcity is deciding what processes you think could work or should work in a post-scarcity world.
One thing that can help in brainstorming such reasons is to recognize that there is no economic competition post-scarcity. One of the primary forces we have weeding out groups of people is that, if you don't provide enough to society, you will be replaced by those who do. If you're making a product for \$100 and someone else can make the exact same product for \$10, you get displaced. In post-scarcity, this does not occur at all. The maker of \$100 items can coexist with the maker of \$10 items.
Typically, to make a post-scarcity world realistic in any way shape or form, one has to consider conserved values such as conservation of energy or conservation of mass. Unless your post-scarcity world has a magical device which produces free energy or free matter, you're going to have a conserved resource. To have a post-scarcity world which has conserved resources is a delicate balance. People must want resources to be distributed exactly as they are distributed. If they were to want otherwise, their thinking would immediately turn to scarcity thinking.
Combining these two points, we see that the people playing The Game do not need to actively contribute to the post-scarcity world in a measurable way, they merely need to not use any more conserved resources than people want them to use. This means their productivity can be virtually 0 and still be accepted, so long as their productivity does not become negative.
Even negative productivity could be accepted in a world without perfect information. It may be that these gamers have an unclear productivity. Maybe they're producing something useful, maybe they aren't. If the civilization doesn't want to reallocate resources in a different way, then they will be left to continue.
Along this vein, their presence may provide a stabilizing effect on the post-scarcity world. They could be a balancing tool to keep resource properly controlled. Or perhaps this civilization is more 1984-esque, and The Game is actually a scarcity distopia designed to show the good citizens what happens if you think in scarcity terms.
Really the answers are endless, but if you properly balance the issues of tying post-scarcity to conserved values, the end result will have value to the reader.