In real life, the dominant male chimps do their best to limit access of other males to the best females, and they are often successful, so they get more chances to breed with the "best" females than other males (interesting bit of trivia--
male chimps prefer older females, as chimps do not have menopause and the older females have greater success rate with offspring being more experienced as mothers and having more status themselves. That's another way the game gets it wrong, as it makes female chimps sterile when they get old, and this doesn't actually happen).
However, as I understand it, the females have their own agenda and don't always cooperate, since it behooves them not to put all their "eggs" in one basket genetically. That's why their breeding system is considered promiscuous and not polygynous. So subordinate males do sometimes get to breed. What I don't know is how often, and whether the dynamic is different in captivity. In the wild, estrus females can go on "safari" (as I believe it is called) where they go away from the group and possibly from the dominant males if they want to mate with a different male. This may be less of an option in a captive group with more limited space.
In fact, even with truly polygynous species, the behavior of the females can affect the success of the males and there is a lot of variation in the dynamics. When a harem gets too large, for instance, or if the females don't "like" the alpha male, they don't always cooperate. And some will breed with "sneaker" males. Or the females are actually focused on resources and the males focus on keeping other males out of a territory where a band of females hangs out more than on controlling the females. It's generally more varied and complicated than an alpha male controlling all the females who just passively follow.
