Semantics don't even matter here. Under the prior CPC, a player can be suspended for conduct generally that reflects poorly on the NFL, whether or not convicted of a crime (see Roethlisberger). Under the new policy "Effective immediately, violations of the Personal Conduct Policy regarding assault, battery, domestic violence or sexual assault that involve physical force will be subject to a suspension without pay of six games for a first offense, with consideration given to mitigating factors, as well as a longer suspension when circumstances warrant." Anyone who believes the new policy to be limited to their definition of domestic abuse needs to read the policy, and understand what the word "or" means. Peterson pled no contest to assault, which is covered by the policy whether or not it is domestic abuse of a spouse.
If we're going to use Big Jim's rule of strict interpretation of the Personal Conduct Policy, then I should first point out that the new policy wasn't enacted until 3 months after Peterson hit his son and therefore might not be able to be applied retroactively.
Second, the policy is vague about whether "physical force" is an element that must be present with
all assaults (or if it is only associated with sexual assault). Since Peterson
did not use any physical force when disciplining his son, the policy may not apply to his case.