If you're wondering what the big deal is and can't (be bothered to) RTFA,
In the Pokémon games, for example, gamers can give their Pokémon nicknames. When they battle online, they see their opponents' nicknames, communicating without messaging directly. Players often nickname for fun—expressing themselves, cracking jokes, and riffing on memes. Nicknames can also be strategic, used to intimidate, tease, or trick opponents. Either way, Pokémon nicknames qualify as "written messages" exchanged online within the meaning of the act.
They're burying the lede here, they're not saying what kids are calling their Pokémon that is causing the uproar. If I name Pikachu (the yellow pika most commonly associated with the franchise, that uses lightning attacks) "bug zapper," that's not offensive. But if I'm naming him "Free Palestine," I can see how the powers that be might be offended. Or something like that (e.g. "8647", which is to say 86, or kick out, 47, as in the 47th United States president (the current one)).
Anyway, I don't name them either. I remember when Final Fantasy 7 was new and some guys were giving Aerith their sister's name and then getting upset when, well, what happens at the end of Disc 1. The game is 29 years old at this point, but the remakes are still new, so it's probably not a good idea. Those of you who have been gaming a while know that changing Aerith's name to that of a loved one can be... well, not the best idea.