I've never played poker online, but I've played some with friends. For me, the fun is in playing against people you can see because you can read their faces. Could anyone explain how online poker is fun without this talking/visual element?
Playing online lets you engage in a large, dynamic math game.
While I understand the math (I got into playing poker seriously because of an interest in botting -- I found the game more interesting than the programming), I don't approach it from a game theory perspective whatsoever. I run my outs and the pot odds in my head, think about how a win or a loss on a hand will impact me, but I have to weigh that against my instincts and make a decision. My instincts will typically win out.
Even online, you can get very successful reads on people, and you can control the action by learning how the players respond. Because of the nature of online poker -- many, many more hands than in real life, and many more players -- I tend to believe you actually get more inside your opponents' heads (compared to playing in real life), not less, as most people tend to assume.
To respond to the GP, I find online poker fun because it's challenging. There's a constant stream of new opponents, each one with different strategies. For me, it's fun in the same way reverse-engineering is; I have a limited set of information and need to guess the next step before it's taken. The quicker I can get inside the player's head, the quicker I can turn their strategies around on them and either suck them out on my big hands or push them off a small pot with a well-placed bluff.
I see poker as a giant optimization puzzle with a bunch of moving parts. I use a number of math tools--and a few psychological tools--to beat that puzzle.
It's fun because you can still read people's minds. You can predict what they have. You know what the outs are, you get people to fold. You can manipulate their minds and effect behaviors.