No, the Mansion was not total loss. If it were a total loss, they would have to tear down was was left and rebuild. Since it was not "destroyed" or a "total" loss the State of Texas can begin to restore the Mansion.
The charred Texas Governor's Mansion is structurally stable and the first steps toward restoring the 152-year-old historic icon began Thursday after arson investigators lifted their tight cordon on the crime scene.
http://www.statesman.com/search/content/region/legislature/stories/06/13/0613mansion.html
No, the Mansion was not total loss. If it were a total loss, they would have to tear down was was left and rebuild. From your link:
"And just as all the furniture and historical artifacts were out of the mansion and in storage, so were all but a few of the original windows."
That's great news.
So, the Texas Governor's Mansion will not be any less authentic than the White House.
(The interior of the White House was entirely gutted and rebuilt in 1949 - 1952.)
