Title text: I'm a solipsistic conspiracy theorist. I'm sure I must be up to something, and I will not stop until I find out what.
In this comic Cueball believes he is part of a secret society, so secret that he doesn't know anything about the society. His belief in the existence of the society, and that he is a part of it, stem from one contact with an 'agent'. Most people would immediately dismiss the idea of such a secret society, especially with no evidence of its existence, and no knowledge of the goals or even whether it is inherently good or evil.
Six years after being 'chosen', Cueball finds the scrap of paper with an address on, and the can of kerosene. Both of these events are not unlikely, and easily explained as simple coincidences, but Cueball somehow sees this as a command that he must burn down the house. Cueball shows that he is willing to put other peoples lives at risk, destroy property and posessions, and face the possibility of prison all because of one event twenty years prior. To the sane person this is absurd. 
Cueball's belief in the society, his delusional linking of the address and kerosene, and his actions in burning down the house, show how badly he wants to be part of something bigger, and to find meaning in the "Chaos of Life".
The punchline refers to an old grade school/middle school prank (Urban Dictionary: pen 15 club, Pen 15.) You'd typically walk up to an unsuspecting schoolmate and ask him if he wants to join the Pen Fifteen club. You'd tell him that to join, you merely have to write the club name on him. You'd then write "PEN15" on his hand or arm, and everyone would laugh at him because it looks like "Penis". In this case, Cueball fell victim to this prank as a child without ever figuring out the joke.
As for the title text, solipsism is the philosophical idea that only your own mind is sure to exist while other minds can't be really known and so those other minds are not proved to be real.
- [Cueball and a child are talking.]
- Child: What's that on your arm?
- Cueball: The mark of a secret society.
- Child: If it's secret, why tell me-
- Cueball: Because I know nothing. I can't betray them because I don't know who they are. I was chosen by an agent 20 years ago. That was my first and last direct contact. It's safer that way.
- Six years later I found a piece of paper in the street with an address on it. The next day I found a can of kerosene in my garage that I'm sure I never bought.
- [The panel represents these actions by highlighting the mentioned objects in a world of gray.]
- I didn't know whose house it was. I just knew that I'd been given my orders. And I carried them out.
- [A dark figure is silhouetted against a flame.]
- Cueball: I don't know who or what we're fighting.
- Cueball: Maybe we're the bad guys.
- Cueball: It doesn't matter to me.
- Cueball: It's enough to know that there are forces working beneath the chaos of life, and I'm a part of them.
- Cueball: That whatever this "pen fifteen" club is,
- Cueball: I'm in it.