Well the NFL is a company that maintains a particular image and because players of that company are extensions of that image, the NFL wants to maintain a healthy image therefore players are bound by particular codes of conduct. This is different than your average American job where, the company you work for, may not care what you do outside the company so long as anything you do privately, does not interfere with your continued employment with that company.
But because the National Football League is televised and has an image, the NFL wants to maintain an image of entertainment and family friendly. This is a situation where the league doesn't want to appear to be "silent" on issues that deal with domestic violence or drugs. I think also the league doesn't want to seem at odds with "female sensitivity" regarding gender related violence. Also, I'm considering the social perspective on this issue concerning domestic violence.
When Beyonce's sister attacked Jay-Z people applauded Jay-Z's restraint but there wasn't much backlash towards Beyonce's sister. But in this situation regarding Rice, there was much discussion on why men shouldn't hit women and how Rice is much bigger and stronger than her and therefore he should've shown restraint. So there are some societal double standards in the perception of domestic violence and responsive violence (or self-defense). i think the NFL wants to take a stance where it does not want to appear like it condones violence by not responding to the issue.
BTW I made a thread about this and didn't see this one.
In addition, the hiring or firing of a player is not a moral issue, this has more to do with the social politics of being an employee of a large company.