You break the laws of Texas in Texas.
I would say that you have to live by the rules in Texas, regardless of what a foreign nation or the federal government thinks or wishes.
I guess one could always NOT GOT TO TEXAS if he didn’t like Texas laws. Texas didn’t make this guy come there and murder a cop did they?!?
Not quite that simple.
The U.S. is a signatory to a treaty that says that if a foreigner is arrested for a crime, his home country's embassy should be notified. That's a good rule; if U.S. citizens are arrested in Mexico (or China, or anywhere) we would want the U.S. Embassy to be notified.
For Texas to say that it is not bound by that treaty is bad constitutional law (Supremacy Clause) and bad policy (we don't want Mexico to retaliate against U.S. citizens).
Having said all of that, that doesn't mean that this guy goes free. He has had a trial and an appeal, and he's guilty. There should be some remedy for the failure to notify the Mexican Embassy, but setting him free now is not that remedy.