Well paced (You can't beat the game in 5 minutes, but it wont take a week)
Not driven by a single game element, so much as the overall scope of the game. Arrived at mainly through playtesting, I think.
Replayable (The first game isn't your last)
Mostly done through randomized starting positions and a variety of opponents that each have their own strategies / special abilities.
Competetive (The AI doesn't play like a 3 year old)
Most 4X games I've seen do not actually achieve this. AI in a 4X game is a really hard problem; the solution for many games is to keep it as a "dumb" AI but give it numerical boosts (faster production/growth curve). My understanding is that AI is usually developed through trial-and-error and playtesting; start with a fairly simple AI, play until you see it do something really stupid, then figure out how to make it so it doesn't do that stupid thing anymore... and repeat. Not particularly interesting or glorious but it works.
Not repetetive (Such as using the same strategy over and over, or spamming units)
Same as "replayable".
Economical (Not having 7 trillion metal and coins after 10 minutes of play)
Same as "well paced".
Not to much micro-managing
Also arrived at through playtesting. Earlier 4X games actually did have quite a bit of micro-managing, and in fact it could be argued that for SOME players who enjoy that level of control, this is desirable. To cut down on this, it's generally a matter of simplifying the mechanics and automating certain processes. (Note that simply giving the player an option of full hands-on or automating is not optimal; if the automation is just as good as micro-managing then there's no point to letting the player take control, but if it's significantly worse then you punish players for NOT micro-managing.)
Exciting (Necessary?) combat
Unsure what this means. Most 4X games that I've seen (such as the Civilization series) automate combat almost entirely; you choose one unit or stack to move onto an opposing stack, a winner is determined behind the scenes, results are displayed. Entering a tactical or real-time combat map isn't something I've seen before in 4X, as it would likely ruin the pacing by making the overall game take too long.
You stil need to use strategy
As opposed to what, following a single easy-to-find overly-powerful algorithm? Playtesting for game balance to prevent a single unit or tech or strategy or whatever from being overwhelmingly better than the others. Also, some "broken" strategies are really just exploiting weak AI, so the solution to that is to iterate on the AI a bit.
Intuitive interfaces (Civilization 5 is a good example)
UI is a huge topic in general, but core principles of the field apply to 4X games just as they apply to anything else. Since you're talking about a niche genre to begin with, expect your players to be familiar with the major other games in the genre, and start with those games as the basis for your own UI. Obviously this depends on platform, too... 4X for PC is going to have a radically different interface than a similar game on console.
And any other important parts to the Strategy/4X genre
IMHO, decent multiplayer is still an unsolved problem in the genre, due to the tendency for players to micromanage on their turn, thus making the game take forever. (An exception would be games such as the Advance Wars series, that are so insanely simplified and constrained that they can be played multiplayer in a reasonable period of time.)