Research continues ...
I am happy to admit that I my first examinations of modern computer gaming require me to divide it into categories.
The first category describes what I had been pejoratively ascribing to all computer gaming, namely the single player modern computer games. These are the games that require that you click faster, their main feature is violence, or they are yet another civilization-building resource-acquisition game. It covers all (to the best of my limited knowledge) single player RTS, RTT, TBS, TBT, civ, the Sims, combat games, and so on, which make up the bulk of most top hundred computer game lists, I think.
As I have said so many other times with board games that I don't like, far be it from me to try to convince people that they shouldn't like something. I simply want to classify these as puzzles rather then games. Each part of the game is solved, either through trial and error, figuring out the "right" solution, or training your reflexes to hit the right buttons at the right times. After each level is solved, that part of the game is essentially done. Eventually, the entire game is solved, because you have trained your way through it.
It may take a few months. But in the end, it's a puzzle, like Soduko. Violent and gory, but a puzzle. You may like this type of activity more than board games; you may like Sudoku more than board games. But even if they are called "strategy" games, they are not really in the same category of what I would consider strategy games. A game that can be solved in six months is not all that deep.
In the second category are strategy games with AI that simulate an opposing player, such as computer Chess and Scrabble. In fact, RTS and civ games may also weakly fall into this category. With chess and Scrabble computer games, there are games with very good AIs and deep strategy. I hear tell that this is less true for the complicated civ and shooting games. You simply learn what the AI does, and train yourself to work around it. The AI is too stupid to do any better.
The best of these games, such as Chess with a good AI, are certainly more on the lines of what I would consider true games as opposed to puzzles. Assuming that the player finds them fun, they offer some of the benefits that board games offer, such as honing strategic thought. What they miss is still pretty vast, however. Meeting face to face, or playing a board game against another player online, requires human to human cooperation, and all that that entails: etiquette, ethics, manners, and a constantly changing and unpredictable opponent.
The third classification of games are the multiplayer games, which are the online games that you play against one or more opponents. Assuming that you enjoy the games, these games offer as much in every way as any board games, as far as I can tell.
The violent ones, aside from their being visceral, are surely no different from war games, which I consider to be one of the highest forms of gaming. I don't particularly like war games myself, but I respect them immensely. Eurogames, for all the fun that they are, are at least as much, and often more, about playing against the board rather than your opponent. War games, even ones with thick rule books, generally use those rules to offer more options, rather than less. The games are usually wide open and offer many more valid strategic options than Eurogames.
Maybe that's why I don't like them as much. War games offer so many strategic options that I get the feeling (again, with limited experience) that two players playing almost any war game will tend to play "their" type of strategy. The play will look kind of signature from game to game. If you are outclassed in one war game, you will likely be outclassed in most other war games as well.
Eurogames, by limiting the strategic options from game to game, force you to try new things and learn entirely new ways of doing things from game to game. You may be good at one and bad at another.
Anyway, all this is conjecture, and I expect to be rebuked in the comments. Please do, and tell me why I'm wrong.
Anyway, online multiplayer gaming seems to me to be pretty much ideal, at least in theory. But they still have a few drawbacks in practice.
First of all, staring at a computer screen and sitting in a chair without a break is tiresome. Second, computers and connections are still pretty unreliable. Third, the actual games being played online are still pretty limited to killing games. Fourth, the games tend to be endless, instead of having a nice start and end, which encourages gaming obsession. Fifth, you need a computer, a network, and a game subscription. Sixth, it is hard to break, socialize, really meet new people, and so on. There is still a lot to be said about physical presence. Seventh, despite the opportunity to teach etiquette, ethics, and manners, most people are learning them online by them absence, rather than by their enforcement.
So hats off to the idea of multiplayer online gaming. I am interested to see what it does next. In the meantime, board games are in practice what multiplayer online gaming is in theory: intelligent, social, etiquette-rich, and fun.