Constellation

If you use "4X" and "simple downloadable game" in the same sentence, my immediate thought is "Risk variant," and there are many such. Constellation is indeed a simple, downloable 4X game, but features novel and nicely conceived gameplay. No dice here.

At game start, a starmap of linked systems is algorithmically generated (so each game has new topography). Systems are of three sizes (small, medium, large). Your turn consists of clicking on a single planet to place a base there, or increase the size of an existing base; small planets may have only a single base, medium planets two, and large ones three.

A base extends a sort of zone of control to all adjoining systems. Essentially, for systems without bases, the game calculates an influence number for each planet, and for each player. One adjoining base gives you influence 1, two influence 2, and so on. The player with the greatest influence controls the planet. The game ends when all planets are controlled, and at that point the player who controls the largest number is the winner.

In other words, this is a deterministic (non-random) abstract strategy game in which play is through the placement of "bases" (which you could equally think of as "influence stones"). The objective is to control as much territory as possible through influence placement, with strategy dependent on analysis of the randomly-generated network topography and the potential influence of different size nodes on the network.

As such, it's a game with a nice level of strategic depth -- not at the level of Chess, but still non-trivial to play. It's not freeware, but the developer has sensibly offered a full play experience without a time limit; the free version is limited only in that it does not permit 3- or 4-player games, only 2-player ones (with the second player either AI or live, hot-seat style), and in that the full game unlocks some optional "special planet" rules.

If abstract strategy appeals to you, it's certainly worth checking out.