Jon,
The point is the same you describe for a biotop. But the rules assume that an ESA is something declared as such by an authority, not by a golfing entity such as a club. In other words, an authority declares an area as an environmentally sensitive area and such an area is within a golf course. Thus, the club needs to react to such declaration and avoid play from such area.
In the Rules there is no definition of an ESA and, thus, no relief is granted because an area is an ESA. The matter is treated in Decision 33-8/41: "If an appropriate authority prohibits entry into and/or play from an area for environmental reasons, it is the Committee's responsibility to decide whether an environmentally sensitive area should be defined as ground under repair, a water hazard or out of bounds". Although it is not expressly stated, but it is clear that the Decision assumes that the area has been declared as an ESA by the relevant authority and, due to such declaration, the club needs to deal with the matter from a golfing perspective.
The Decision goes on saying that you may not declare the area as water hazard, unless it complies with the definition of water hazard, which in the case of Randy's course it does not.
In addition, at the end of the Decision it is stated that such an area should be fenced or the like, in order to prevent players from entering the area.
Applying this to the case of Randy's course in Chile, declaring an area which is not ESA as such is unnecessary to deal with the issue presented by those areas and perhaps even against Decision 33-8/41. They should be treated as ground under repair, out of bounds or leave them as they are now.
I hope this clarifies the issue from the point of view of the rules.
Best,