You could have it up to the player. The player hits a button that they wish to retire/submit/end the game, and are then given some sort of score.

Fiction wise, it depends a bit on your setting, are you on some sort of wildlife preserve, a ranger or something? In which case the button might act as summoning some sort of wildlife organization to come in and do an evaluation of the species survivability. If it's humans in a plague ridden quarantine area, it could be contacting a WHO or government agency to convince them that what you have setup is sustainable.

Edited the original post to give more info.

Edit: just going to add a bit more info to help you get a idea of the game, the species is dragons, and the setting is medieval fantasy, the creatures trying to kill off the dragons are a combination of beasts, and humans. The dragons can build things, but they're mostly simple things, like caves and such, as the dragons are quadrupedal.

Given this, two possible "win-conditions" that come to mind are the already-mentioned case of wiping out the enemy, and of forging a peace with the enemy (well, with the humans, at least; we might presume that with human allies the beasts may become a lesser problem). Such peaces might have a variety of forms--for a few examples:

• If the dragons grow sufficiently strong, they might strong-arm the humans into servitude and tithes taken from the populace
• If the two populations are of similar power, an alliance might be formed--dragon-riders come to mind.
• If the humans are the stronger, the dragons might barter for their lives with servitude, perhaps working to power forges and heat homes, or providing shock-troops for human armies.

There is a particular piece of ancient lore, passed down from dragon to dragon since time immemorial. An egg incubated and hatched in magma can birth a mighty Dragon Queen. Very few eggs can withstand the intense, continual heat; it is not a process to be undertaken lightly. Even if the birth is succesful, the process leaves the child frail and weakened for decades. Worse, she will bend the very fields of magic around her, so that all the wise will know of the birth. The enemies of the dragon, even rival dragon lineages, will attack en masse to stop the fledgling threat. But once she reaches maturity, the Dragon Queen's powers will be unmatched and she will lead the dragons to renewed dominance of the world.