I agree that the help center page could make it look like this question is off-topic, but I think it's on-topic for this site. A key point from that page is,
The above list is not exhaustive, so if you feel your question is about earth science, go ahead and post it.
so, in that respect, the user was following the guidelines in posting the question.
In the past we've used a rule of thumb that if the subject is covered by the AGU or EGU, then it's on-topic here. For example, we used this to agree that questions about planetary atmospheres, such as Mars and Venus, are on-topic even though they would also be on-topic for Physics.SE and possibly Astronomy.SE. Similarly, there was a meta question about ecology where the answer was "it depends"; some ecology questions are suitable for here, some are better suited at Biology.SE.
Ultimately, that entropy question is asking about global energy flows and biogeochemical cycles, which is very much on-topic for this site. I've spent a lot of my career working on climate and the global carbon cycle (e.g., photosynthesis, biomass), but I think of myself as an Earth system scientist rather than a biologist. In my experience, a lot of people working in this area have math and physics backgrounds and self-identify in a similar way.
The real question here is whether this site has enough experts to answer the question. Thematically, they might be here but we're quite a small community and that leads to knowledge gaps and unanswered questions. I know some of us here could have a stab at an answer, but it might not be an expert answer. Biology.SE is much larger and more active, so maybe this question would get more attention over there. I don't know.
At the very least, it looks to me like our help center page here at ES.SE needs to be updated to include "biogeochemistry" or "biogeochemical cycles" in its topic list.