Texas doesn't have the death penalty for the crime of driving while intoxicated. The man in Texas was charged with murder because he killed people with his car. Yes he was driving drunk but had he simply been pulled over and failed a breathalyzer, he would not have been charged with anything that carries a possible death penalty.

Presumably the OP is referring to a death penalty solely for the crime of DUI.

Singapore has the death penalty for possession of many types of drugs, including <2 oz of marijuana. But as far as I can tell they don't execute for DUI.