doesn't necessarily mean he is a Texas resident.
There are two possible explanations. One is that he is a Texas resident. The other, more likely, explanation is that he is committing tax fraud in Texas. I suspect that Walker is also claiming a homestead exemption for a house in Georgia.
The Texas' Comptroller's web site states:
To qualify for the general residence homestead exemption an individual must have an ownership interest in the property and use the property as the individual's principal residence. An applicant is required to state that he or she does not claim an exemption on another residence homestead in or outside of Texas.
Similarly, the homestead exemption in Georgia is only available for the owner's principal residence.
https://dor.georgia.gov/property-tax-homestead-exemptions Logically, you cannot have more than one principle residence - that's what "principle" means.
The Texas application for a homestead exemption contains a verification that the homeowner does not claim a homestead exemption in another state. (I can't seem to post that link.) I am unclear whether the submission of a false claim for a homestead exemption in Texas is a misdemeanor or a felony. Odds are ain't nobody in Texas going to prosecute Walker for a felony.