Having now played First Empires seven times on a review copy from Sand Castle Games, I'll say that Vogel has succeeded in creating a world conquest game that encourages you to be aggressive. Each of the 2-5 players takes charge of a civilization on an alternate Earth, and over the course of 7-8 rounds, you are rewarded for controlling regions that match the dice rolled at the start of your turn (which typically requires you to kick someone out of those regions), for meeting the requirements on achievement cards (typically by picking on others), and for conquering opposing cities or having your own cities on the board at game's end, both of which require you to move into new regions.
You are rewarded for acting selfishly and taking whatever regions suit you best. If others lose their land, well, they haven't lost any people on the board because opposing forces retreat instead of being removed from play — and sometimes you can use a retreat to your advantage since you retreat to any one region where you already have a presence. As in Beyond the Sun, a "loss" in one region allows you a free teleportation to somewhere else, which can be a great thing in a game that initially limits you to 2-3 movement points at the start of the game.
Combat in First Empires is a simple thing: If I can move more people into a region than you have there, you must leave. The dice I roll (and possibly re-roll) at the start of my turn feature five colors that match the colors of Earth's regions and a sword. Should I have one or more swords on a turn, those swords stand in for my people — one person with three swords = four people — allowing me to conquer a region by sending in fewer people (and therefore spending fewer movement points). How does one person wield three swords? Presumably by spinning them really fast like a propeller, but that is left as an exercise for your imagination.
So swords are great, right? Except they often aren't, especially in the first couple of rounds when everyone is huddled in their starting city and plenty of empty land lies available for the taking with only one person. What's more, by holding regions that match the color on rolled dice, you advance on civilization tracks, which gives you better stats and more endgame points — and swords are not a color, so they allow you to take over regions more easily at the expense of not having as many colors on hand to boost you on tracks.
You can choose to discard an achievement card from your hand to change a die to a sword or a sword to a color of your choice, and the rules encourage you to do the latter in the opening turns because your civilization is initially feeble. Every advancement on a civilization track boosts your chance for future growth by giving you more dice, more re-rolls, more movement, more people, or more achievement cards. Yes, you can discard an achievement card to get an achievement card, earning points in the process, and this realization is critical for you to overcome the trap of valuing potential points in hand more than actual (but fewer) points in reality.
While combat in First Empires isn't random, other elements of the game are, with the die roll at the start of your turn being the most prominent. If you roll (or re-roll) colors that match regions in which you already have a presence or can reach or take over easily, then great, you'll advance on your civ tracks, which will boost you in future turns. If not, well, you can throw away your starting achievement card to ensure that you advance on two tracks in the first round — which means you're down a card compared to lucky opponents.
After seven games, I'm still not sure how large a role the rolls play in someone's success as the game is relatively short, and the general feeling is one of trying to maximize the opportunities available to you rather than developing a plan and sticking to it no matter what. You might have a general plan, sure, and that will determine which dice you re-roll, but you need to focus on advancing somewhere as the game lasts only 7-8 rounds, so you don't have a lot of time in which to progress.
For details on how to play, what changes based on player count, and more thoughts on the gameplay experience, check out this overview video: