I share your disdain for the DSM, but since it's so prolific, I can't really fault other resources that use it. Especially since these kinds of internet things can't really provide any help directly besides recommending that you go talk to a doctor/therapist about whatever problem it thinks you have, it pretty much has to be based on the DSM, because the doctor/therapist is going to be using the DSM.

For example, anytime I see someone asking about a problem that sounds like initiation deficit (a matter close to my metaphorical heart), I'd like it if I could tell them it's called initiation deficit, tell them the name of a condition that entails that symptom, recommend they see a doctor about that condition, maybe mention some common treatments. But there doesn't seem to be anything in the DSM that has initiation deficit as part of the diagnostic criteria. So instead, I give them some ADHD-related anecdotes and maybe some suggestions on how to reword the description of the problem so it sounds like a concentration issue.

DSM aside, the test often asked some weird questions. I think there were a few where you have to be knowledgeable about psychology/psychiatry in order to understand what kind of info it was looking for. (I think this is sometimes a problem in actual diagnostic interviews too!)

The kind of depression I have would fit your definition of a mental disease... but pretty much all of the depression-related DSM diagnoses could apply to that kind of disease OR to being sad because your life sucks.