tl;dr: Since illegal hits in a game involving consensual violent contact are foreseeable and since penalties for such have been agreed upon by private parties, no players engaging in bounties for foreseeable on-field actions should be criminally liable. Motive for causing injury is legally irrelevant.
In general, if you intentionally hit someone, you are guilty of a battery (a criminal offense)
However, there are circumstances where your behavior is "excused" -- two of the most common excuses are (1) you are defending yourself from an aggressor and (2) the "victim" gave his consent for you to hit him
Undoubtedly, every NFL player has given his consent to be hit during a game by any other NFL player during the course of a game just like a boxer gives his consent to be punched by an opponent.
Now, there are certain "hits" that are not within the rules of the game -- faskmasking, chop-blocking, hands to the face, spearing, late hits, scuffling, fighting, etc. Consequences for illegal hits are executed both during and after games. Penalties range from yellow flags to fines and suspensions.
Every player recognizes that illegal hits are natural by-products of a violent game where large men are moving at full speed with the intent to cause contact. That is, these types of "illegal" hits are foreseeable actions by opposing players. There is implicit legal consent for players to be hit illegally to the extent that the penalties for such actions are essentially contracted for, as proscribed by the NFL rulebook and by the commissioner, who is the final arbiter of any penalties.
Therefore, foreseeable hits carried out on the football field, whether "legal" or not according to the rules of football, are governed by rules agreed-upon by private parties, as opposed to public criminal statutes and common law.
Unforeseeable hits, which are those that would be wholly unexpected on a football field, would not be consented to and therefore, would be governed by public law. For example, it is entirely unforeseeable to be shot or stabbed on the football field. Neither action has a rational connection to the game of football, and players would not be expected to assume the risk of such actions occurring in the course of a game.
On the "intent" issue...
That a given player indends to cause violent contact carrying a high risk of hurting or injuring another player is enough to establish "scienter", or the knowledge of wrongdoing.
It is immaterial whether a player's intent is to simply tackle or block, to harm, or to injure, another player. Legally, we don't care since the consented actions of players inherently carry an extremely high degree of violence and risk of injury. Likewise, when general intent is established, the motivation behind the intent -- e.g., monetary reward -- is irrelevant. Motive plays a part in homicide, not battery.
Essentially, the only legal reason for criminally prosecuting players who have agreed to bounties on other players is that the consent to hit such players was obtained through "fraud." That is, a bountied player has not consented to other players receiving monetary rewards for injuring him.
But this is a weak argument given that intent to cause grave and violent contact on every play of every game has already been consented to. Illegal hits (i.e., the effects of bounties) that have the sole intent of injuring another player are already governed by agreed-upon rules and regulations of the NFL.
So while the NFL is well within its rights to punish any sort of conspiracy for producing illegal hits, the contractual/consensual nature of the foreseeable on-field activity renders players immune from criminal prosecution in any event.