Number one is fine. Number two isn't very well phrased, because it suggests that the natural environment itself is constructing the tourist facilities!

In spoken English both would generally be understood, the first form is a little more clear since you are using "construction" as a noun. If you just end the sentence "The natural environment is damaged by construction.", then it would still make sense if you wrote In this case construction is the direct object. "The natural environment is damaged by constructing", then it would sound incomplete on its own.

1 is more accurate and it is the right answer ....