You need to define what you mean by "being a zero-sum game". For example, in terms of entropy (which is a possible metric in the context of "dissipation") it isn't a zero-sum game -- certain processes increase entropy more, some less. In terms of total instantaneous thermal absorption, which defines the temperature of the Earth, it also isn't a zero-sum game -- If there was a white surface and it is made black, then the temperature of the Earth will rise; the same goes for emitting CO2 which in effect increases the global absorptivity (energy that wouldn't be absorbed if the Earth didn't contain as much GHG). Putting solar cells in barren deserts isn't going to disrupt local lifeforms simply because there aren't any. So it seems in almost every definition of zero-sum it indeed isn't a zero-sum game -- which is good!
Note that I didn't claim renewable energy has no environmental cost. It most definitely has. Every activity will have certain impacts, greater or lower, on resource availability, thermal balance, and on other lifeform habitats. The key is pricing adequately those impacts so any damage could be repaired or compensated. The effect of pricing is usually just impact minimization, since the cost of repair or compensation is usually much greater than prevention.
So it is a matter of seeking technologies that give the greatest return (power output in this case) for total cost (environmental and economic) -- and better alternatives than current ones are constantly being discovered, thankfully.