Heres from the site you gave as your proof that there is no Sharia law in Texas.
The court ruled that everyone in the case signed an arbitration agreement to use a certain set of arbitrators. Certain set of arbitrators aka TEXAS ISLAMIC COURT, 888 s. Greenville Ave., suite 188, Richardson, Texas. Then states that the Second Court of Appeals upheld the ruling of the TEXAS ISLAMIC COURT, 888 s. Greenville Ave., suite 188, Richardson, Texas.
Yep, no creeping Sharia in Texas for sure. /s
Trying to explain the difference between a court and an arbitration is probably not worth the time, effort or bandwidth. But you might consult an attorney to explain it to you.