I think the problem is less that lots of mouse clicks and so on are required to play computer games, but that it often increases exponentially as the game progresses. For example, I'd say my "ETA" to 1 AD in a marathon civ4 game is 4 hours...and I'd also say that's how long it takes me to play a golden age from the Taj Mahal, as I'll check every city every turn so as to make sure I don't waste any part of it. I don't mind some micromanagement, but it needs to increase in a more linear manner. While making the UI count go down where reasonably possible would be great, dropping 100 clicks out of 1000 at one point in the game isn't going to change the exponential problem as long as it's dropping 10 out of 100 at the earlier point. Even if I'm having fun with a long game, the realization that it will take me several hours in the endgame to go through as many years as were in one turn at the beginning of the game can become a deterrent to continue playing. Exactly how long later in the game doesn't really matter as much since, while an hour or two saved from better UI is nice if I notice it, what I'm noticing more is how little time it took in the early turns of the game.
I don't, however, by any means wish for any sort of AI to control what I do until it's, well, actually intelligent - while I think it's excellent for AI, if I was going to miss any more than a turn I'd have a hard time choosing between letting the AI do its thing and just putting the workers to sleep and my cities in anarchy. In fact, I'd much rather grab a friend that I know is good at games but has never played civ before, give them enough instructions so that they know enough to play and let them have at it for a few turns.
While there's the military reasoning, I still think that the "rule of seven" seems entirely arbitrary - and far too small. He mentions chess - yes, it has sixteen pieces per player, but it can actually become more complex with fewer pieces! Managing several large stack of units often isn't really that big of a problem - partly because they've been grouped together, but as long as they're active I don't find large numbers too problematic. In fact, I often move every unit individually once I've split up a group even if I could reform it, partly because I enjoy making tactical maneuvers if I'm playing well. I've easily had not just more than sixteen "pieces", but more than sixty on my "chess board" in a game of civ and it's rarely been a problem...and when it has been, the inactive units have been more of one. Different people can manage different numbers of "units" and some certain types better than others - thus giving players better options as to what, how and how much they manage would be better than having some ideal management amount.
What I think could help the problems would be better ways of implementing non-AI delegation, which would probably require better notifications and queues. I don't queue many buildings on civ4, for example, as I prefer to still check the city screen when a building finishes - but it would make for less management if I could have the option, enabling me to skip checking when I know I don't want to and making it faster when I do. Being able to set the number of turns to build something and then switch to something else would be great, too. It would be helpful to have notifications for city growth, an option to inspect the city, and, particularly, a queue for which tile to work next. Go to orders could be queued, too. Other changes and improvements to the general way the interfaces of games work could help streamline some of the management issues.
As another example, I'd love to be able to organize my inactive units better with a set of "group/select/wake ___ units" - by location, unit type, city/non-city, etc. In the case of the civ3 railroad dilemma, being able to outline an area of the map, select all workers in that area and then pair them up would be delightful, but not unreasonable to expect. Adding in "build railroad from point a to b" might be even more delightful, but I wouldn't consider it reasonable to expect both due to the increased specificity in the nature of the order and the fact that I wouldn't trust the computer to build the railroad quite where I wanted it. The same might go for adding a "go to this city" order to a unit when it's built, but certainly not "go to whichever of city x, y or z will have the fewest units when this would arrive". Again, the general idea would be to delegate tasks to the game through simple ways to issue and change multiple orders rather than having to delegate to an AI.
I don't necessarily expect games to have a "perfect" way to manage everything, though. If a game is designed well it should become more fun as it gets more complex. Games won't sell because they won't get played if they're overly complex. Sure, sometimes a reasonably complex game will get to be a drag, but there's nothing wrong with taking a break from a game and coming back to it. Certainly I don't think civ4 should be dumbed down in any way - nor given more to the AI to control any more than the player wishes, no matter how good the AI is. No game should ever be a matter of speed of or determined by button mashing, but certainly some amount of button mashing should be just fine.