You are misunderstanding it. Don't worry though, yours is a common misunderstanding! So common, in fact, that the Wikipedia article on arousal starts with, "not to be confused with sexual arousal".
In psychology, "arousal" is a technical term and not all arousal causes harm. In fact, many forms of arousal are quite healthy. Being awake, for example, is a type of arousal and most people stay awake for 16+ hours per day without issue.
Now, you are correct that sexual arousal is a type of arousal, but there is no reason to believe that sexual arousal would cause the pathology of arousal that is discussed in the paper. In fact, the specific section you linked refers to "hyperstable arousal regulation" which refers to a tendency for a person's level of arousal to remain too constant over time rather than varying appropriately to the situation they are in. And on top of all that, causation is not indicated. There is no reason to believe that the arousal is causing the depression rather than the other way around.
Got it and thanks for clarifying. I also amended my last comment since I had a bit of extra time to read the study more thoroughly. I'd be quite interested to see which way the causation goes. Although I suspect that hyperstable arousal may be a symptom of depression rather than a cause of depression, I have heard that the intense adrenaline rush of skydiving may alleviate depression for some people. To me this suggests there may be a way to break out of that hyperstable arousal state by intentionally reaching a state of extremely high arousal, perhaps ending a bout of depression early.