I've never even read that book, but I probably should. As it's described in the article, I see many parallels with today's anonymised internet culture - we can be someone else, someone who doesn't have to fear any consequences for what he says, we can lie on the internet to (try to) form other's perception of ourselves, thus being whoever we want to be. But ultimately it's still the same person making those decisions…
And in the book, the distiction is a bit different: whatever someone does in "real life", his body, face, voice... it's all the same. In small villages it's impossible to hide. In bigger cities at that time, it wasn't so big, people still know each other among his social circle. And it was easy to notice someone leaving his own circle and appearing in another.
So, what internet gives you as a basic (easy to be anonymous, in the sense that commmon people perceive it, I'm not talking about using tor and so on), Jekyll had to blame on his drink. And blaming saves his face: wasn't he blaming it, he couldn't say that the "monster" was doing things that, in the end, he was trying to.... hyde.