Roll Through the Ages is Matt Leacock's second game, his first being the wonderful Pandemic, and it is already clear that Matt has no intention of being "typecast" as a designer. Pandemic was a purely cooperative game; Roll Through the Ages is competitive. Pandemic was a board game with cards; Roll Through the Ages is a die-rolling game with no board. Pandemic required no material components other than what comes with the game; Roll Through the Ages requires you to keep score with pencil and paper on a special scoresheet. The two games share little in common, so it is clear that Leacock can work with a broader range of mechanics than many practicing designers.
And yet, there is a clear similarity between the two games, in that both were clearly created by a guy who is a user interface designer at his day job; there are multiple play aids and references for both games, such that you almost don't need the rules to play... just follow the instructions on the components in front of you. This attention to the game's "interface" would appear to be a game design signature of Leacock's, and one that digital and non-digital game designers alike could learn from.
I describe Roll Through the Ages as "Civilization meets Yahtzee." You start with three "cities" (dice) and roll them, then can reroll any or all of your dice up to twice. The faces of these dice show resources such as food (required to feed your cities each turn, else you take a victory-point penalty), workers (used to build more cities to get you more dice, or build monuments for victory points), and trade goods and coins (used to purchase special abilities, such as getting +1 food per die or getting an extra reroll, which additionally give victory points). At the end of the game, sum up the points, highest score wins.
For the most part, Roll Through the Ages is indirect competition (as with Yahtzee). You roll your dice, record your score, and then pass the dice to the next player; you are not directly attacking other players, and on their turns you mostly sit around and wait for your turn again. To the extent that players affect one another, it is mostly about reacting to what your opponents are doing. If one player builds a particular monument, other players get only half points for completing the same monument later, so building part-way towards a particular monument is both an aggressive move (dissuading the opponents from building there) and a risk (someone might get a ton of workers and be able to finish it before your next turn). If one player looks like they're trying to trigger the end of the game, other players may shift from a long-term building-up to a shorter "grab all the points I can now" strategy. In some rare cases, your die rolls affect other players (modified by two of the many special abilities). And so on. But for the most part, you're trying to maximize your personal score and hoping that you do a better job than your opponents.
On the game's official website, you can download the scoring sheets for a variant that extends the play time but also adds a trading element to the game, which adds a bit more player interaction if you like Catan-style trade mechanics.
Either way, a game of Roll Through the Ages takes less than an hour to play, and each turn offers some interesting risks and tradeoffs that change based on board position. For people who want to play a civilization-building game but don't have all weekend to devote to a single game, you could do much worse.