In a bold move, I'm going to put the summary first because this is a very long post. I have stayed away from concepts like strategic depth and, god forbid, fun because they are hard to define in useful terms. So in terms of easy to define properties, I think good board games tend to have:
- fuzzy player rankings
- limited options at each decision point
- no medium term decisions
- low randomness
- no elimination
- frequent activity
The first four games listed all have clear win conditions (get the most victory points) but at any given stage it is difficult to tell how many victory points a given player has. In Dominion for example it would be possible to track what every player's score is, but the victory point cards are scattered throughout the deck so it isn't possible to do a quick count. Alhambra uses a scoring track but scoring is sporadic enough that it indicates roughly who is in the lead but not the final outcome. The advantage of doing this is that it adds an air of excitement to the final tally at the end of the game. It also means that players can think they are in the running for victory for much longer, which means nobody sulking in a corner. Of course it does mean that the game can't have a victory point threshold as its ending condition (as is used in Settlers of Catan for example).
Puerto Rico is a game in which the players take a lot of decisions about a lot of different things over the course of the game (roles, trading, building, colonising, etc, etc). What the game does well is offer very few options to choose from at any given decision point. This streamlines the game and limits the damage of players who agonise over every decision they have to make. Providing the game is well designed in the interactions between the various elements, small decision sets should still be able to give players the ability to control the flow of the game.
No Medium Term Decisions
Alhambra allows the player to pick which tile/money they get short term, which will affect the structure of their Alhambra in the long term. However, the medium term decision of where to place the tile for maximum effect is deferred by the remodel phase so that it can become a short term decision. So what? Without any evidence or training, my suspicion is that in games people make short term decisions quickly because the risk/reward is clear and affected by few if any unknowns. Long term decisions are often made before the game even starts, or upon seeing the opening setup. Medium term decisions are the most difficult because you have a reasonable idea what will happen, but it is clouded by the moves available to other players between the time that decision is made and the next time you get to act. Medium term decisions are where the combinatorial explosions in options occur, and so are the ones that people take the longest to take. If you want to make decisions easy for people, make sure the outcome is obvious or so far away as to be of no concern.
Games, especially board games, benefit from some randomness. It helps bring lagging players back into the game and means strategies have to be modified on the fly so that games play out a bit differently every time. On the other hand, you need to keep the amount of randomness low. Any joy gained from luck in a game on one player is visited in equal measure as frustration on another player, and if there is a high degree of randomness then luck becomes more important than ability. In Torres, each player has a deck of about a dozen special effect cards, with each player having the same cards. When drawing an action card, the player gets to draw three and then pick one. After that the discarded cards are placed on either the top or bottom of the deck, at the player's discretion. So there is a small amount of randomness, you might not get the card you want in a given turn, but you will almost always get a card you can make some use of.
One of the worst things that can happen in a game is to get eliminated early (in something like Risk or Monopoly, for example). If people have got together to play some games, then you are left sitting around waiting for the game to finish. For those left in the game, they either lose a person for the next game, or there is somebody moping around until the current game ends.
One of the problems of the epic board games like Risk is that you often go anywhere up to half an hour without getting to do anything. By contrast in Dominion, you often haven't finished shuffling the deck before it's your turn again, while the phase/turn structure of Puerto Rico means that each player is acting every one or two minutes. This structure keeps the player's interest and I think tends to make for shorter games because there is less wasted time.
I don't know if you could build a game from these elements alone, but I think you could definitely take a game and improve it by introducing some of these gameplay properties.