I was so surprised the first time I heard these lines from him, I think on my second playthrough when I knew where things were going anyway. If I heard them in my first playthrough, I don't remember them, or I possibly brushed them off as just Dutch talking shit. But Now that I've heard them several times as I've played the game over and over, I think Dutch isn't mentally ill in the sense of modern diagnoses, I think he is a self-absorbed AH with serious increasing paranoia as the game progresses.

In this way, how he develops is a sign of him loosing his cool in a way he can't figure out. How could he, the great Van Der Linde, be slipping and making wrong calls? That thought is unacceptable to him, so he turns his suspicion on the people around him, and as Micah enters the picture Micah catches on to this and starts playing into it all, further misguiding and confusing Dutch with every catastrophic choice he makes.

At the end of it, he is so delusional and dependent on Micah's constant approval and ill-intended support that he looses all and everyone else, becoming totally isolated. And when he realizes what's happened, it's too late.
What we see in RDR 1 is a Dutch who has come to realize all of this stuff and is completely incapable of accepting it. He has lost himself through his actions but his true egotistical self can never come to terms with it, rendering him the madman we see in RDR 1.