Yup, many missing details.
Called police? I would think they did. . . and followed the burglar, as they want to get their possessions.
As you pointed out, this is Texas where you have the right to protect yourself and your property, up to and including, deadly force.
Watching the burglar and following him is not unusual and I, personally, see nothing wrong with that.
” ... he and his brother were able to track the intruder down a few blocks away... “
Good thing this is Texas and not Mass., or the UK