In all likelihood the standard NFL boilerplate contract contains a "morals clause" which is broad and which gives the NFL all kinds of power to have its way in matters like this. Rice voluntarily accepted the terms of his contract in exchange for millions in compensation. It's pretty cut and dried to me.
I think this is right. While the wisdom of allowing Goodell to make these decisions can certainly be questioned, the NFL certainly has the right to suspend a player for behavior they feel is detrimental to the image of the NFL.
Ring the bells that still can ring
Forget your perfect offering
There is a crack, a crack in everything
That's how the light gets in - Leonard Cohen