Is this a situation that the jurisdiction requires the victim to personally press charges?
Eventually, yes. Most everywhere (in the US) the DA is not going to go forth with a case involving violence, outside of maybe political hot-button cases like domestic violence, without the victim pressing charges. Even with DV cases, if he victim is hell bent on not testifying (he or she really can't get out of it if they are called) or downplaying or outright lying (something no one will be able to prove), the DA isn't going to waste his or her time. Too much other work to do and cases to prosecute.
However, most people don't know that you can not be arrested in Texas without a warrant unless the arrest falls under certain situations. The most common exception is a peace officer actually viewing the offense, so ANY offense he views, even if it is a Class C and would offer no jail time as a penalty, could serve as the basis for a legal arrest. Incidentally, forget the term false arrest, at least in Texas. No such thing. There are legal and illegal arrests. False arrest is common law torts, and I'm not even sure it is a valid civil cause of action in Texas -- it may be but under another name. But I digress (sorry).
Anyway, the officers working security that saw the incident could very well have placed the player under arrest if they had jurisdiction and if their department allowed it (and I'm sure it was yes to both). That is why you hire police officers for security. I don't know if they did, but at this point it doesn't matter. He was charged and now has to surrender or he will have a warrant issued. If he appears, he'll be fingerprinted and make a bond. He may or may not be arraigned -- not sure at that level of criminal offense. But either way, if the official does not want to proceed with the charges, they will be eventually dropped. Hopefully it will at least be after the player is out the 15 percent fee for the bond and attorneys fees.
There are also civil causes of action the Referee has -- against the player and in my opinion, (POSSIBLY) against the coaches and school district. Going against the district is tricky as they have statutory immunity to some claims, another reason why that needs to be abolished. He may or may not want to go after district employees. But that's the thing I don't like about immunity: say there's an issue as to what the school district did and a coach or AD did. The district might get off Scott free but the employee doesn't have such immunity. They will, however, get the benefit of the school district's legal defense team if it comes to that.
I say take them down. This crap must end. NOW.