"Game" and "Non-Game" are simply classifications of animals. They both still fall under the purview of TPWD and any lawmaker can introduce a bill to amend the regs to make specific rules that apply to just these animals.That doesn’t apply in this instance. They are not game animals in the state of Texas.
Any attempt to do this or anything close to it would be met with immediate lawsuits that would (correctly) strike down TPWD’s overreach. That is one of many reasons why that idiotic plan would NEVER happen.
Being classified as non-game doesn't magically exempt them from regulation. Not having seasons for exotics IS the regulation currently codified for TPWD.
They can just pass a law with new regulations for hunting a specific species exactly the exact same way they did to make it legal to hunt them from a helicopter or making it legal to kill pigs without a hunting license like they did in 2019.