Is a defective headlight considered a moving violation?

While laws vary from state to state and jurisdiction to jurisdiction, normally citations for things such as a burnt out headlight are referred to as defective equipment citations and normally are not considered moving violations, as they usually, also, do not carry any points. In many locales if you get the defect repaired within so many days and appear at the police department or court you might even be able to get the citation dismissed.

It is not a moving violation. Get if fixed and bring proof of the repair to court. You may get the case dismissed, paying only court costs.

This is an equipment violation. Texas requires headlights to be activated when light or atmospheric conditions (aka fog) make it difficult to see 1000 feet in front of you. If you believe this could be a point of contention, you may hire a lawyer to fight this for you.