I'm not assuming that at all. My model is extremely simplified so it would fit into a comment, but it doesn't need to be that simple for the general idea to hold.
Suppose you pirated a thousand games and would've legitimately purchased one. Your piracy then represents a theft of one game. Since there's no way to tell which one game you would've bought, we could simplify it to say that stole one one thousandth of a game from each publisher (assuming they were all unique publishers).
In reality, I think it's really hard to know what you would've done without access to piracy. It's almost certainly not "buy all the games" but it's also probably not "buy zero games".
I also pirated a lot of things when I was in college - partly because it was cheaper, and I was very cheap, and partly because it was easier than actually getting some things. One thing I try to do is separate my own personal bias (it can't be bad because I did it) from what seems like the clear harm and moral reasoning I laid out above. You're taking from the publishers, even if only small values, and if everyone did what you did, publishing couldn't exist as a business.
I think it makes sense that poor people would steal more frequently. They need to. It also makes sense that younger people would steal more frequently - they are less mature, think less about others, and less about the consequences. Given that, it doesn't surprise me that you and I both pirated more while younger. That said, even though it makes sense, that doesn't mean it's right.